Consider randomly selecting a student who is among the 12,000 registered for the current semester in a college. Let X be the number of courses the selected student is taking, and suppose that X has the following probability distribution: x 1 2 3 4 5 6 7 f(x) 0.01 0.02 0.12 0.25 0.42 0.16 0.02 a. Find the cdf of X. b. Find the expected number of courses a student is taking this semester. c. Find the variance of X. d. Find the third quartile of this distribution.

a)

b)

4.61

c) 1.1579

d) 5 is the third quartile of this distribution.

Step-by-step explanation:

We are given the following discrete distribution:

a. Find the cdf of X.

Probability of X being less of equal to x. Than

b. Find the expected number of courses a student is taking this semester.

Multiplication of every outcome by its probability.

c. Find the variance of X.

Multiplication of the squared subtraction of each value and the mean, multiplied by its probability. So

d. Find the third quartile of this distribution.

100*(3/4) = 75th percentile

The cdf passes 0.75 when X = 5, so 5 is the third quartile of this distribution.