Answer :
Answer:
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.
