Question

The pdf of weekly gravel sales X was f (x) =

{
3/2 ( 1 - x²) , 0 < x < 1
0, otherwise
What is the expected value?
A. 3 /2
B. 1
C.0
D. 3 / 8

Answer 1

The expected value of the weekly gravel sales is 3/2.

Step-by-step explanation:

To find the expected value of a random variable, we need to multiply each possible value x by its corresponding probability f(x) and sum them up. In this case, the possible values of x are between 0 and 10. For 0 < x < 10, the probability density function (pdf) is given by f(x) = \frac{3}{2}(1 - x^2). For all other values of x, the probability is 0.

We can calculate the expected value as follows:

1. Multiply each value of x between 0 and 10 with its corresponding probability f(x)
2. Sum up all the products

Doing the calculations, we find that the expected value is 3/2 or option A.