If a random variable X has a probability mass function P(x) = cases kx^2, & for x = 1, 2, 3, 4 0, & otherwise cases , then the mean of X is ...

Step-by-step solution

The sum of all probabilities must be equal to 1 . _ x=1 ⁴ P(x) = 1 k(1^2 + 2^2 + 3^2 + 4^2) = 1 k(1 + 4 + 9 + 16) = 1 30k = 1 k = 1 30 The mean of the random variable X is given by E(X) = _ x=1 ⁴ x P(x) . E(X) = _ x=1 ⁴ x(kx^2) = k _ x=1 ⁴ x^3 E(X) = 1 30 (1^3 + 2^3 + 3^3 + 4^3) E(X) = 1 30 (1 + 8 + 27 + 64) E(X) = 100 30 = 10 3 = 3.333 Answer: 3.333