1 pt The following density function describes a random varia

(1 pt) The following density function describes a random variable x. A. Find the probability that x lies between 2 and 4. Probability = B. Find the probability that X is less than 3. Probability =

Solution

A. Find the probability that X lies between 2 and 4.
Integrate the density function between 2 and 4

(1/8) ? (x-1) dx , limits are 2 to 4
= (1/8) [ x^2/2 - x] between 2 and 4
= x^2/16 - x/8 between 2 and 4

Let F(x) = x^2/16 - x/8
F(4)-F(2) = 0.5 -0 = 0.5
The probability that X lies between 2 and 4 is 0.5

B)
Find the probability that X is less than 3.
Integrate the same density function from 1 to 3
Let F(x) = x^2/16 - x/8 (see problem A)
F(3)-F(1) =0.1875 - (-0.0625)
=0.25
The probability that X is less than 3 is 0.25.