# Probability & Statistics Important Questions Short

UNIT-I

SINGLE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS

1 If X & Y is a random variable then Prove E[X+K]= E[X]+K ,where ‘K’

2. Write the properties of the Normal Distribution?

3 Explain probability distribution for discrete and continuous?

4 If X is Discrete Random variable then Prove that Var (a X +b) = a2 var(X)?

5 Write the properties of the Normal Distribution?

6 Write the importance and applications of Normal Distribution?

7 Define different types of random variables with example?

8 Derive variance of binomial distribution?

9 Derive mean of Poisson distribution?

10 Explain about Moment generating function?

UNIT-II

MULTIPLE RANDOM VARIABLES, CORRELATION ®RESSION

1 State the properties of joint distribution function of two random variable?

2 Explain about random vector concepts?

3 If a random variable W=X+Y where X and Y are two independent random

4 Explain types of correlations?

5 Write the properties of rank correlation coefficient?

Taxonomy

6 Write the properties of regression lines? Understand 7

7 Write the difference between correlation and regression? Knowledge 7

8 The rank correlation coefficient between the marks in two subjects is 0.8.

The sum of the squares of the difference between the ranks is 33. Find the

9 Find the angle between the regression lines if S.D of Y is twice the S.D of

10 Derive the angle between the two regression lines?

UNIT-III

SAMPLING DISTRIBUTIONS AND TESTING OF HYPOTHESIS

1 Explain different Types and Classification of sampling?

2 Write about Point Estimation, Interval Estimation?

3 Write a short note on Hypothesis, Null and Alternative with suitable

examples?

4 Write a short Note on Type I & Type II error in sampling theory?

5 Prove that Sample Variance is not an Unbiased Estimation of Population

Variance

6 Write Properties of t-distribution?

7 Explain about Chi-Square?

8 Write a short note on Distinguish between t, F, Chi square test?

9 Explain about Bayesian estimation?

10 Compare Large Samples and Small sample tests? Create

UNIT-IV

QUEUING THEORY

1 Explain queue discipline?

2 Explain pure birth process?

4 Derive expected number of customers?

5 Derive average waiting time in queue?

6 Apply P(n>1) ?

7 Define transient state and steady state?

8 Explain M/M/1 model?

9 Explain M/M/1 with infinite population?

10 Derive probability of having n customers Pn in a queue M/M/1, having

poisson arrival?

UNIT-V

STOCHASTIC PROCESSES

1 Define stochastic process Knowledge

2 Explain different types of stochastic process

3 Give examples of stochastic process Create

4 Find the expected duration of the game for double stakes

5 Define Markov’s chain

6 Explain Markov’s property

7 Explain transition probabilities

8 Explain stationary distribution

9 Explain limiting distribution

10 Explain irreducible and reducible