Answer to Question #48731 in Statistics and Probability for Tot

Question

1) Let the r.v’s X1 and X2 have the joint density f(x1,x2 ) (x1,x2 )={█(K, 0≤X1<1 and 0≤X2<1- X1 or 0, e.w)┤
what is then value of K ?
what is fx1 (x1 ) ?
what is fx2 (x2 ) ?
is x1 and x2 independent? Justify.
2) Let Z ,W , be i.i.d. rv.’s exponentially distributed with parameter λ. If Y=Z+W. What is
The pdf f(Z,W) (z,w)?
The pdf fY (y)?
The expected value E[Y]?
3)Let the r.v. X be uniformly distributed in the interval [-2π,2π]. Given that Y=X^4. Find fY (y)

4) Let the r.v. =√(X^2+Y^2 ) , an W=X/Y Find f(z,w) (z,w).