Data Science Interview workshop

author: Chinki

date: 26 Feb 2016

Question-01

How can you generate a random number between 1 - 7 with only a die?

Chinki's Solution

Random numbers should have equally likely probability to come. so roll dice twice and take sum, exclude numbers more than.

Question-02

In any 15-minute interval, there is a 20% probability that you will see at least one shooting star. What is the probability that you see at least one shooting star in the period of an hour?

Chinki's Solution

This is example of poisson distribution. with lamda=15 mint Shooting start

p(x>=1)= 1-P(x<1) = 1 - P(x=0) = 1 - (0.8)⁴ =0.5904

1-(0.8)^4

[1] 0.5904

Question-03

How can you get a fair coin toss if someone hands you a coin that is weighted to come up heads more often than tails?

Chinki's Solution

I will generate random 10 trails and figure out how much is weighted to head.

Question-04

You have a 50-50 mixture of two normal distributions with the same standard deviation. How far apart do the means need to be in order for this distribution to be bimodal?

Chinki's Solution

Binomial distribution can be approached to normal if n is large. mean of binomail=np

mean of 50-50 mixture = n1p1+n2p2

Question-05

A certain couple tells you that they have two children, at least one of which is a girl. What is the probability that they have two girls? ( Data Scientist at Color Genomics)

Chinki's Solution

This is conditional probabilty problem s ={BB, BG, GB, GG } p=1/3

Question-06

You call 2 UberX's and 3 Lyfts. If the time that each takes to reach you is IID, what is the probability that all the Lyfts arrive first? What is the probability that all the UberX's arrive first?

Chinki's Solution Total=5 p( 1st car is lift)=3/5 p( 2nd is also lift)=2/4 P( 3rd is also lift)=1/3 and is used

Question-07

A lazy high school senior types of application and envelopes to n different colleges, but puts the applications randomly into the envelopes. What is the expected number of applications that went to the right college

Chinki's Solution

P(correct envelope)=1/n=X Correct envelope Y = sum(X) E(Y)=n.E(X)=n*1/n = 1

Question-08

Let's say you have a very tall father. On average, what would you expect the height of his son to be? Taller, equal, or shorter? What if you had a very short father.

Problem-09

Do gradient descent methods always converge to same point?

Question-10

What is a confidence interval and how do you interpret it?

Chinki's Solution

I am 90% confident that the value will be in this interval.

Question-11

What is the difference between confidence interval and probability interval?

Chinki's Solution

Confidence interval- I am 90% confident that my value will be in this interval. Probability Interval- 90% probability that value will fall in this interval.

Question-12

What's the difference between a MOM, MLE estimator? In which cases would you want to use each?

Chinki's Solution

MOM is the method of moments approach to find estimator of the parameter. MLE is maximum likelihood estimator

Question-13

What is a p-value? What is the difference between type-1 and type-2 error?

Chinki's Solution

The p-value is used as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected.

https://www.investopedia.com/terms/p/p-value.asp

Type I - Rejecting null/ Null true Type II- Accepting null/ Alternative true

Question-14

What is logistic Regression and what is linear regression?

Question-15

which variables will you use if two variables are highly correlated and dependent in logistic regression?

Question-16

Can you please explain to me the difference between a parametric and non-parametric test as if I did not know anything about it?

Question-17

What are the different ways to find the error in predictive models?

chinki's Solution

MAE and MSE

Question-18

How do you explain SD to a common man?

Question-19

tell me about Bayes Rule? (Data Scientist at C3 loT)

Question-20

Do you know central limit theorem?

Question-21

According to the central limit theorem, If data is large then it will follow the normal distribution then whats the use of other distribution? Because in the industry you will get large data only?

Question-22

Where to use Median OR Mean? (Data Scientist at Here Technologies)

Question-23

The difference between Bayesian vs frequentist statistics.( Data Scientist at Yelp)

Qusetion-24

What is PDF and CDF for any distribution? (Data Scientist at 6sense )

Question-25

Die A has orange on one face and blue on ???ve faces, Die B has orange on two faces and blue on four faces, Die C has orange on three faces and blue on three faces. All are fair dice. If the three dice are rolled, ???nd the probability that exactly two of the three dice come up orange?

Chinki's solution

A (1O,5B)
B (2O,4B) C (3O,3B)

(A Orange * B orange * C blue ) + (A blue * B Orange * C orange)+( A Orange * B orange * C Blue )

1/6*2/6*3/6 + 5/6*2/6*3/6 + 1/6*4/6*3/6 (6/216+30/216+12/216)=48/216=0.222

Question-26

Roll a fair four-sided die twice, the die has sides 1,2,3,4 and let X be the maximum of the two outcomes or equal to the outcome when the outcomes have the same value. Write down the p.m.f. for X and ???nd the ???rst moment about the origin?

Chinki's

X 1 2 3 4 f(x) 1/16 3/16 5/16 7/16 E(X) = 1/16 + 6/16 + 15/16 + 28/16 = 50/16 = 3.125

Question-27

Consider the birthdays of the students in a class of size 30. Assume that the year consists of 365 days?

How many di???erent ordered samples of birthdays are possible allowing repetitions (with replacement)?

The same as part (a), except requiring all the students have different birthdays (without replacement?

Chinki's solution

a- (365)³⁰ b- 365P30

Question-28

What is the difference between Supervised Learning an Unsupervised Learning? (Predictive Analyst Quora)

Question-29

How can outlier values be treated?

Question-30

What is polynomial Regression? and do we use it frequently?

Question-31

what is correlation?

Question-32

Let A and B be events on the same sample space, with P (A) = 0.6 and P (B) = 0.7. Can these two events be disjoint?

Chinki's Solution

Disjoint P(A)+P(B)=1.3

Question-33

A roulette wheel has 38 slots - 18 red, 18 black, and 2 green. You play five games and always bet on red slots. How many games can you expect to win?

Chinki's Solution

5*18/38

Qusetion-34

The number of miles that a particular car can run before its battery wears out is exponentially distributed with an average of 10,000 miles. The owner of the car needs to take a 5000-mile trip. What is the probability that he will be able to complete the trip without having to replace the car battery?

Chinki's solution

X follows exponential distribution with mean 10000

P(X > 5000)= 1- P(X <= 5000)= 1 - (1- exp(-5000/10000))= exp(-½)

exp(-1/2)

[1] 0.6065307

Thank You !!!