The probability distribution of a random variable X is Compute the mean, variance, and standard deviation of X.

Question

The probability distribution of a random variable X is  Compute the mean, variance, and standard deviation of X.

Quizplus · Accepted Answer

To find the mean, we need to integrate x*f(x) from -infinity to infinity:

Mean (μ) = ∫x*f(x) dx = ∫x*11e^(-2x) dx from 0 to infinity = 1/2

To find the variance, we need to integrate (x-μ)^2*f(x) from -infinity to infinity:

Variance (σ^2) = ∫(x-μ)^2*f(x) dx = ∫(x-1/2)^2*11e^(-2x) dx from 0 to infinity = 1/8

Therefore, the standard deviation (σ) = sqrt(σ^2) = sqrt(1/8) = sqrt(2)/4

Thus, the best choice is (B), 11eab448_e7b3_d9bc_acdb_199e45ff401e_TB6027_11.

The Probability Distribution of a Random Variable X Is