Math 354 Mathematical Statistics Worksheet #1 Name
1. Xhaspdf/(x)= 6ea",0<x< oo. Find P(X< 2).
2. A die has sides 1, 2, 3, ..., 6.
a) Its rolled twice. If 6 > 4, nd P(the sum is 6).
b) Its rolled ten times. Find P(exactly two 2s are rolled).
3. We hav
Math 354 Mathematical Statistics Examples
Result 1: Suppose thatX has pdf f (x;6) and the range of values X can take does not depend on 0.
Let Z =%ln(f(x;t9)). Then E[Z]=0 and Var(Z)=E|:%Z].
1. Verify that E[Z] = O and Var(Z) = E[1 Z ] for the special
Math 354 Mathematical Statistics Examples
Neyman Pearson Lemma: Suppose we are testing H 0 :6 = 60 vs H I :6 = 191 and the test that
if f(x19x2 a-"9xn;00)
< C has signicance level oz| and power K1091). Then any
f(x1,x2 ,..., x" ;9,)
rejects H 0
other