problem 1:
a) State the prove Lehmann-Pearson Lemma. Give its significance in testing of hypothesis.
b) Construct a LR test to test H_{o}: µ = µ_{o} against H_{1}: µ ≠ µ_{o} in sampling from N (µ, σ^{2}), where both µ and σ^{2} are unknown.
problem 2:
a) describe Kolomogolor-Sminnor one sample and two sample tests.
b) Describe the term Mann-Whitney U-test.
problem 3:
a) Show that SPRT terminates finally with certainty.
b) Define the term OC and ASN functions of SPRT. Derive them for testing the proportion of a binomial distribution.
problem 4:
a) State and prove the Wald’s fundamental identify.
b) describe the Wald’s SPRT. Derive OC and ASN functions for testing the mean of a normal distribution with unit variance.
problem 5: prepare brief notes on any two of the given:
a) Factorization theorem.
b) CAN estimators.
c) Monotone likelihood ratio and UMP tests.
d) Median test.
e) SPRT for testing Poisson parameter.