Let f(x) = ( x^3/5000)(10 - x) and x be a variable contained in the interval [0,10] and f(x) = 0 for any other value of x. a. Prove that f(x) is probability density function. b. Find its cumulative distribution function. c. find p(1<=x<=4) d. show that P(x=6)=0 e. draw a diagram that correctly resembles each of the case (c, d, e)