[SOLVED] EE5342 Homework1

For this problem the observation Y = (Y₁,Y₂) is a vector of two random variables Y₁,Y₂. The hypotheses are as follows

H₀ : Y₁ ∼ N(3,1),Y₂ ∼ N(−1,1) H₁ : Y₁,Y₂ ∼ P_x,

where N(µ,σ²) is the Gaussian distribution with mean µ and variance σ², and P_x is the distribution with the following probability density function

, for all x ∈ R.

In both the hypotheses, the random variables Y₁ and Y₂ are independent of each other. Use uniform cost, i.e., C₀₀ = C₁₁ = 0, C₁₀ = C₀₁ = 1.

You must use Monte Carlo simulation to find and plot V (π₀) versus π₀, for π₀ = 0.1,0.2,…,0.9.

Simulation Details:

• For each value π₀, you must generate 10⁶ instances of Y and apply the Bayes decision rule to perform detection. Use the average cost of these 10⁶ instances as your estimate for V (π₀).
• In each instance, you must randomly generate Y according to either H₀ (with probability π₀) or H₁ (with probability 1 − π₀).
• Ensure that the observation vectors generated for H₀ and H₁ indeed satisfy the probability distributions described above.
• Reference value: at π₀ = 0.25, V ≈ 0.