MTH136/STA114: Statistics

Homework #7

Due: Wednesday, Mar 21, 2001

1. DeGroot Chapter 8 Section 1 Page 441 Problems 1, 2, 3
2. DeGroot Chapter 8 Section 2 Page 452 Problems 11, 14
3. The random variables X₁, ..., X_n are independent with a Poisson distribution with mean theta. We are unsure which of

   H₀: [theta=1] H₁: [theta=4]

   is true, but begin with Prior Probability ½ for each.
   • Find the posterior probability of H₀ if we observe X₁, ..., X_n.
   • With n=5 and {X_j}={5,3,9,5,2}, find the likelihood function L_x(theta) and the Likelihood Ratio r(x)=L_x(4)/L_x(1)
   • With n=5 and theta=1, find the probability that the likelihood ratio r(x) exceeds the value observed above.