Let X1 and X2 be a random sample of size n = 2 from the

QUESTION:

Let (X_{1}\) and \(X_{2}\) be a random sample of size \(n=2\) from the exponential distribution with pdf \(f(x)=\) \(2 e^{-2 x}, 0<x<\infty\). Find

(a) \(P\left(0.5<X_{1}<1.0,0.7<X_{2}<1.2\right)\).

(b) \(E\left[X_{1}\left(X_{2}-0.5\right)^{2}\right]\).

Equation Transcription:

Text Transcription:

X_1  

X_2  

f(x)= 2e^-2x,0<x<infinty  

P(0.5<X_1<1.0,0.7<X_2<1.2)  

E[X_1(X_2-0.5)^2]