Quiz_3_Questions - Test 3 Questions 1. If Y is an...

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Test 3 Questions 1. If is an exponential random variable with pdf Y ( ) exp{ / 3}/ 3, 0 fy y y = −> , then find a number t (to three decimals) so that . ( ) 0.05 PY t >= 2. Suppose are independent exponential random variables with mean 1 100 ,..., YY 2 θ = and . Use the central limit theorem to estimate . 100 1 j j S = = Y 0 (| 200 | 20) PS 3. Suppose is a standard gaussian random variable. Find a number c (to three decimals) so that . ~( 0 , 1 ) ZG () 0 . 2 PZ c 4. We are given that and 12 0 ,..., ~ (0,1), independent ZZG 1 i a = + is i is even and if i is odd. Then if , find (to three decimals) . 1 i a =− 20 1 (1 ) i i Ta Z = =+ i ( 2) PT > 5. Suppose we can model the number of claims per week of a certain type of insurance policy as a Poisson random variable with mean λ . In a 10 week period,
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