X has a probability distribution function fx35e35x whenever

X has a probability distribution function f(x)=.35e^(-.35x) whenever x is greater than or equal to 0 and is 0 otherwise. Find each of the following probabilities:

P(x>.15)

P(x<.35)

P(.3<x<1.86)

Solution

P(x < 0.15)= .35e^(-.35x)dx with limits from 0 to 0.15 = 0.05545

now P (x > 0.15) = 1 - P(x < 0.15) = 0.9489

P (x < 0.35) = 0.1153

P (x < 0.3 ) = 0.0996

P (x < 1.86) = 0.4784

P(.3<x<1.86) = 0.379