Problem 1 The number of pages in a homework assignment submi

Problem 1. The number of pages in a homework assignment submitted by an INEG 2313 student is equally likely to be any of the values in (2,3, ... ,9}. Let X denote the number of pages in a randomly selected homework assignment. (a) What kind of random variable is X? (b) What is the probability that a randomly selected homework assignment has four pages? (e) Determine the probability that a homework assignment has at least six pages. (d) What is the expected number of pages in a homework assignment? (e) What is the standard deviation of the number of pages in a homework assignment?

Solution

X is uniform RV

P(x=4) = 1/8

P(x<=6) = P(x=2) + P(x=3)+....+P(x=6)

P(x<=6) = 5/8

Expected number of pages,

E(x) = Sum of x* P(x)

E(x) = 1/8 * 2 + 1/8 * 3 + .....+ 1/8*9

E(x) = 1/8 ( 2+ 3 + ....+ 9)

E(x) = 1/8 * 44

E(x) = 5.5