Total No. of Questions 10] [Total No. of Pages 01
M.Sc. DEGREE EXAMINATION, MAY 2018
First Year
STATISTICS
Probability and Distribution Theory
Time 3 Hours Maximum Marks :70
Answer any five questions.
All questions carry equal marks.
Q1) Define continuity axiom of probability. Explain.
What is mathematical Expectation? Explain in brief.
Q2) State and prove inversion theorem.
State and prove cantelli lemma.
Q3) Explain Chebyshev and Khintchin's laws in brief.
Explain the convergence of sequence of random variables.
Q4) State and prove Levy and Lindeberg form of central limit theorem.
Explain the types of convergence with interrelations.
Q5) What is moment generating function? Explain its characteristics.
Explain the characteristics of discrete distribution.
Q6) Write the properties of interrelations of multinomial.
What is compound binomial? Explain in brief.
Q7) Define lognormal distribution. Write its characteristics.
Write about logistic distribution. Also find its mean and variance.
Q8) What is probability generating function? Explain in brief.
Derive moment generating function of Laplace distribution.
Q9) Explain probability density function of a single order.
Derive the joint p.d.f. of …..
Q10)a) Derive the distribution of non-central chi-square.
Define order statistics and obtain the distribution.