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Let Z1 and Z2 be independent standard normals. The random vector (X1, X2) is said to have the bivariate normal distribution with parameters /1, /2, p, 1 and 02 where X1 = M1+olZ1 X2 = /2 + 02pZ1+ 02\\/1 -p2Zz. (a) Using this definition, derive (meaning: show the derivation of ) the joint pdf of X1 and X2. (b) In the easiest way possible compute E(X1), E(X2) and E(X1X2). (c) Derive the conditional pdf fx, x2($1|x2) of X1 given X2 = 12. This will turn out to be a normal distribution. What are its mean and variance