Description

Department of Electrical Engineering and Computer Sciences
EECS 126: Probability and Random Processes
Discussion 12
1. Hypothesis Testing for Bernoulli Random Variables
Assume that
• If X = 0, then Y ∼ Bernoulli(1/4).
• If X = 1, then Y ∼ Bernoulli(3/4).
Using the Neyman-Pearson formulation of hypothesis testing, find the optimal randomized decision rule r : {0,1}→{0,1} with respect to the criterion
min
randomized
s.t.
where β ∈ [0,1] is a given upper bound on the false positive probability.
2. Joint Gaussian Probability
Let X ∼N(1,1) and Y ∼N(0,1) be jointly Gaussian with covariance ρ. What is P(X > Y )?
1