A Px

Solution

Prob between x=a and x=b is the area under the density curve above x axis.

The density curve has x intercept 4 and y intercept 0.5

Hence equation is

x/4+y/0.5 =1 or

x+8y = 4

WE are going to use that for finding this prob

a) P(x<1) = Area between x=0 and x=1

When x=1 y = 3/8

Hence area of trapezium between 0 and 1 is

1/2(1/2+3/8) = 7/16

P(2<x<3)

x=2 means y = 1/4

x =3 : y = 5/8

Hence area between 2 and 3 = 1/2(1/4+5/8) = 1/2(7/8)=7/16

x is atleast 3 means prob is area between x=3 and x=4

y value for x=3 is 1/8 and for x=4 is 0

Hence area of right triangle = 1/2(1)(1/8) = 1/16