Question

hink about a density curve that consists of two straight-line segments. The first goes from the point (0, 1) to the point (0.7, 1) then the second goes from the point (0.7, 1) to the point (1.3, 0). a. Sketch this density curve: b. What is the probability that X falls below 0.5? c. What is the probability that X lies between 0.7 and 1.3? d. What is the probability that X lies above 0.2? e. What is

Answer 1

b. 0.5

c. 0.3

d. 0.8

Explanation:

A. See attached for the Sketch of the density curve

b. probability that X falls below 0.5 = area under section from 0 to 0.5

=0.5 *1 = 0.5

c. probability that X lies between 0.7 and 1.3 = area of the triangular section from 0.7 to 1.3 = 1/2 * (1.3-0.7)*1= 0.5* 0.6 = 0.3

d. probability that X lies above 0.2= area under section from 0.2 to 0.7 + area of the triangular section from 0.7 to 1.3 = (0.7-0.2)*1 + 1/2 * (1.3-0.7)*1

= 0.5 + 0.3 = 0.8