Question

Random Variable Transformation:

Suppose is a random variable with {} = 100 and ²{} = 60. Let W = 150 + . Thus, {W} and ²{W} = a. 100 ; 60 b. 100 ; 210 c.

Answer 1

The mean and variance of the new random variable W, defined as W = 150 + X, are found by adding the constant 150 to the mean of X and squaring it and adding it to the variance of X, respectively.

Step-by-step explanation:

The given problem involves transforming a random variable. We are given that the random variable X has a mean of 100 and a variance of 60. We are asked to find the mean and variance of the new random variable W, defined as W = 150 + X. To find the mean of W, we simply add the constant 150 to the mean of X. So, the mean of W is 150 + 100 = 250. To find the variance of W, we need to square the constant 150 and add it to the variance of X. So, the variance of W is 150^2 + 60 = 22600.