For the probability density function shown what is the proba

For the probability density function shown, what is the probability of the random variable x being less than 4?

Solution

This is the total area from x = 0 to 4.

Getting the area of the rectangle from x = 0 to 3,

A1 = 0.1875*3 = 0.5625

Getting the area from x = 3 to 4

A2 = 0.125*1 = 0.125

Hence, the total area is

P = A1 + A2 = 0.5625 + 0.125 = 0.6875 [ANSWER]