A random vector (X, Y, Z) has joint density given by f (x, y,z) = k exp
Fantastic news! We've Found the answer you've been seeking!
Question:
A random vector (X, Y, Z) has joint density given by f (x, y,z) = k exp [− 1/2 (2x2 − 2xy + y2 + z2 + 2x − 6y) .
1. Compute k.
2. Compute the expectations P(X), P(Y ) and P(Z).
3. Compute the density of the random vector (X, Z).
4. Compute the correlation coeffificient between X and Z and between X and Y .
5. Let W = X + Z; compute the probability density of W.
Related Book For
Mathematical Statistics with Applications in R
ISBN: 978-0124171138
2nd edition
Authors: Chris P. Tsokos, K.M. Ramachandran
Posted Date: