Question

Let X, Y, and Z be three independent, identically distributed random variables, each with density function f(x). Determine:

a) The mean of X+Y+Z
b) The variance of X+Y+Z

Answer 1

The mean of X+Y+Z is 3 times the mean of one of them, and the variance of X+Y+Z is 3 times the variance of one of them.

Step-by-step explanation:

a) The mean of X+Y+Z is equal to the sum of the means of X, Y, and Z. Since X, Y, and Z are identically distributed, their means are equal. Therefore, the mean of X+Y+Z is 3 times the mean of one of them.

b) The variance of X+Y+Z is equal to the sum of the variances of X, Y, and Z. Since X, Y, and Z are independent, the variances of X+Y+Z is equal to 3 times the variance of one of them.