Find the expected value of the continuous random variable X associated with the probability density function over the indicated interval.

Question

Quizplus · Accepted Answer

The expected value of a continuous random variable X with probability density function f(x) over the interval [a,b] is given by:

E(X) = ∫(a to b) [x * f(x)] dx

In this case, we are not given the specific probability density function f(x), so we cannot solve the integral. However, we are given the interval [0,4].

Looking at the choices, we see that only option C has the value 2, which is the midpoint of the interval [0,4].

Intuitively, we know that for a symmetric probability distribution over an interval, the expected value should be at the midpoint of the interval. Therefore, we can confidently choose option C as the correct answer.

Find the Expected Value of the Continuous Random Variable X