Question

Let X₁,...,X₁₀ be a random sample from N(θ₁,1) distribution and let Y₁,...,Y₁₀ be an independent random sample from N(θ₂,1) distribution.

Let φ(X,Y ) = 1 if X < Y , −5 if X ≥ Y , and

V=
  φ(X_i,Y_j) .
1. Find v so that P[V>=v]=0.45 when  $\theta$₁=$\theta$_2.

2. Find the mean and variance of V when $\theta$₁=$\theta$_2.

10 10 2

Answer 1

iid indep en derd 411,7) as a Yandam Saw ple from N(A:02,1) pome m,4) E(V)50 discrete rr ealoulati m.