Consider the function f : R® — R defined by0 z3where c is an undetermined constant.(a) For what value of ¢ is f a probability density function?(b) Suppose that a continuous random variable X...

<>< 1.5="" c(3="" −="" x)=""><><="" 3="" 0="" x="">(a) For what value of c is f a probability density function?
(b) Suppose that a continuous random variable X has probability
density function f. Compute EX. (Hint: Draw a picture of the
pdf.)
(c) Compute P(X > 2).
(d) Suppose that Y ∼ Uniform(0, 3). Which random variable has the
larger variance, X or Y ? (Hint: Draw a picture of the two pdfs.)
(e) Determine and graph the cumulative distribution function of X.<>


Consider the function f : R® — R defined by 0 z<0 cx=""><><15 t@="1" cs-2)=""><><3 0="" x="">3 where c is an undetermined constant. (a) For what value of ¢ is f a probability density function? (b) Suppose that a continuous random variable X has probability density function f. Compute EX. (Hint: Draw a picture of the pdf.) (c) Compute P(X > 2). (d) Suppose that Y ~ Uniform(0, 3). Which random variable has the larger variance, X or Y? (Hint: Draw a picture of the two pdfs.) (¢) Determine and graph the cumulative distribution function of X.