Csider a binary hypothesis-testing problem involving h1

Question

Question: 1. Consider a binary hypothesis-testing problem involving H1: θ = θ0 versus H1: θ = θ1. Suppose that there are two sensors providing two sets of observations {X1, X2, ..... ,Xn} and {Xn+1, Xn+2,.... ,X2n} for making the decision. We assume that the observations under each hypotheses are independent, identically distributed with density p(x|Hj),j = 0, 1, with

p(x|H_i) = θ_j exp(-θ_jx)u(x)

and θ0 = 1,j = 0,1. Here u(x) is the unit step function. We can consider two schemes for processing the observations in order to arrive at a decision regarding which hypothesis is correct:

1. A centralized scheme where the 2n observations from the two sensors a-·_;used together to make the decision.

2. A decentralized scheme in which at each sensor site, a decision is made using only the observations available at that site.