How do you define variance in terms of Mathematical expectation?

State the definition of Mathematical expectation using continuous random variable.

Let X be a random variable and Y = 2X + 1. What is the variance of Y if variance of X is 5 ?

Prove that,  V(aX) = a²V(X)

The time to failure in thousands of hours of an important piece of electronic equipment used in a manufactured DVD player has the density function
\(f(x)= \begin{cases}2 e^{-2 x}, & x>0 \\ 0,& \text { otherwise }\end{cases}\)
Find the expected life of this piece of equipment.