Questions are attached. Thank you for helpin!

For the probability density function f(x), find the following values. f(x) = 12x2(1 - x) on [0, 1] (a) E(X) = X (b) Var(X ) = ( c) o (X) =\fIn a 4-year study, the number of years that a patient survives after an experimental medical procedure is a random variable Xwith probability 3 2 density function f(x) = aX on [0, 4]. (3) Find the expected survival time E(X). E(X) = 3 I (b) Find P(1 s X s 4). W): If the number of years until a new store makes a profit (or goes out of business) is a random variable X with probability density function f(x) = 0.75x(2 x) on [0, 2], find the following. (Round your answers to three decimal places if necessary.) (a) the expected number of years E(X) E00 = (b) the variance and standard deviation Var(X) = 17(X) = (c) P(X 2 1.5) m 15> = l:]