Find the values of c to make the following fimetions valid probe- Nay density functions. (a) (5 Paints) f(x)= cfgl —x)}-, for 0< x< I (Hint the derivative of sin-'(x)= v.,=) (b) (5 points) f(x). ceop(—x — for x e R (5 Points) f(x)= C(5.x' — coa(x)) for 00 x51 Question X is a uniform random variable distributed on [0, 'xJ. Find the pdf of Y = sinX. Question .5.
Question *a. Let X be a Bernoulli random variable with P(X = 0) = I — p, P(X = I)= p. Let Y = I — X and Z = XY. (a) (5 points) Fuld P(X = x, Y = y) for x, y, e (0, (b) points) Find P(X = x,Z = z) for […]