Question: Let X, Y be i.i.d. with distribution Binomial(n,p). Let U = X +Y, V = X Y. Com pute the joint probability mass function of

Let X, Y be i.i.d. with distribution Binomial(n,p). Let U = X +Y, V = X Y. Com pute the joint probability mass function of (U, V). Are U, V independent? Determine the conditional probability mass function of U given V = 7), namely pg(u | V = 7)). Let X,Y be i.i.d. with distribution N(0, 1). Let U = X I Y,V = X Y. Compute the joint density function of (U , V). Are U , V independent? Determine the conditional density function of U given V = 7), namely fU(u | V = v)

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