A continuous random variable X has probability density function f(x) = k * x^2 for 0 ≤ x ≤ 2, and 0 elsewhere. What is the expected value E[X]?
Answer and explanation
Correct answer: D. 3/2
- Step 1: Find k: ∫_(0 to 2) k x^2 dx = k [x^3/3]_(0 to 2) = 8k/3 = 1 => k = 3/8.
- Step 2: E[X] = ∫_(0 to 2) x * f(x) dx = ∫_(0 to 2) (3/8) x^3 dx.
- Step 3: (3/8) [x^4 / 4]_(0 to 2) = (3/8) (16 / 4) = (3/8) 4 = 12/8 = 3/2.
Practise more Probability.
Free questions with an explanation for every one, and full timed GATE mock tests.
More Probability questions
- A continuous random variable has the probability density function for , and elsewhere. W…
- Two fair dice are thrown. What is the probability that the sum of the numbers is ?
- Two fair dice are thrown. What is the probability that the sum of the numbers is ?
- Two fair dice are thrown. What is the probability that the sum of the numbers is ?
- Two fair dice are thrown. What is the probability that the sum of the numbers is ?
- Two fair dice are thrown. What is the probability that the sum of the numbers is ?