please solve 3.4(8,12,13) in details as soon as posible.

Cos(O). 3.4-87 A random variable X can have values - 4, -1, 2, 3, and 4, each with probability 5. Find: (a) the density function, (b) the mean, and (c) the variance of the random Y= 3X'. 3.4-9. A gaussian random variable, for which fx (x) = (2/ Jm ) exp(-4x? ) is applied to a square-law device to produce a new (output) random variable Y = X-/2. (a) Find the density of Y. (b) Find the momers m, = E[Y], # = 0, 1,.... (Hint: Put your answer in terms of the gamma function (fined in Problem 3.2-27.) 3.4-10. A gaussian random variable, for which X = 0.6 and g, =0.8, is transformed to a new random variable by the transformation 105X