Probability & Statistics Important Questions Short
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?
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?
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?
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
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
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
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
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