Suppose that contamination particle size (in micrometers) can be modeled as can be modeled as $$f(x) = 2x-^3 for 1 < x. Determine the mean of X. What can you conclude about the variance of X?

Mean = 2

What i can conclude about the variance is that it doesn't exist.

Step-by-step explanation:

We want to determine the mean of "X".

So first of all, let the probability density function (f) of the random variable X be;

f(x) = 2x^(-3)

This can be simply written as;

f(x) = 2/x³, x > 1

Thus;

Mean E(X) =(∞,1∫)2/x³ (xdx)

= (∞,1∫)(2/x²)dx

Integrating, we have;

E(X) = - 2/x at (∞,1)

Thus E(X) = (-2/∞) - (- 2/1)

= 0 + 2 = 2.

So mean E(X) = 2

Variance E(X²) = =(∞,1∫)2/x³ (x²dx)

= (∞,1∫)(2/x)dx

Integrating, we find that x becomes 1 and thus there's no way to apply the boundary (∞,1). Thus, the integral can be said to be diverging and thus doesn't exist.

Since the integral doesn't exist, the variance doesn't also exist.

make sure you have version 2.50

try looking in the very back of the book : )

step-by-step explanation:

you can download it here