Question

Let X denote the amount of space occupied by an article placed in a 1-ft³ packing container. The pdf of X is below.

f(x) =

90x8(1 − x)		0 < x < 1
0		otherwise

(a) Graph the pdf.

Obtain the cdf of X.

F(x) =

0	x < 0
x9(10−9x)	0 ≤ x ≤ 1
1	x > 1

Graph the cdf of X.

(b) What is P(X ≤ 0.65) [i.e., F(0.65)]? (Round your answer to four decimal places.)


(c) Using the cdf from (a), what is P(0.35 < X ≤ 0.65)? (Round your answer to four decimal places.)


What is P(0.35 ≤ X ≤ 0.65)? (Round your answer to four decimal places.)


(d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.)


(e) Compute E(X) and σ_X. (Round your answers to four decimal places.)

E(X)	=
σX	=

(f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.)

Answer 1