15. Let X denote the amount of space occupied by an article placed in a 1-ft3 packing container. The pdf of X is f(x)
90x8

(1  x) 0  x  1 0 otherwise

a. Graph the pdf. Then obtain the cdf of X and graph it.

b. What is P(X  .5) [i.e., F(.5)]?

c. Using the cdf from (a), what is P(.25  X  .5)? What is P(.25  X  .5)?

d. What is the 75th percentile of the distribution?

e. Compute E(X) and X.

f. What is the probability that X is more than 1 standard deviation from its mean value?