Question

Let X be a continuous random variable with a parameter λ > 0 and with a probability density function (pdf) function f(x) = λe^(-λx) for x ≥ 0, and f(x) = 0 for x < 0. Which of the following expressions gives the expected value for X?

A. ∫(-[infinity], [infinity]) x²λe^(-λx) dx

B. ∫(0, [infinity]) xλe^(-λx) dx

C. ∫(-[infinity], [infinity]) (x-λ)²λe^(-λx) dx

D. ∫(-[infinity], [infinity]) xλe^(-λx) dx

Answer 1

The expected value for a continuous random variable can be calculated using the formula: E(X) = ∫(x * f(x)) dx. Therefore, the correct expression which gives the expected value for X is option B: ∫(0, [infinity]) xλe^(-λx) dx.

Step-by-step explanation:

The expected value for a continuous random variable can be calculated using the formula:

E(X) = ∫(x * f(x)) dx

Therefore, the correct expression which gives the expected value for X is option B: ∫(0, [infinity]) xλe^(-λx) dx.