Question

Suppose you have four independent and identically distributed random variables X1 through X4 . Each Xi is distributed N(12,8) . Find the mean and variance of Y= ?

Answer 1

To find the mean and variance of Y, add up the means and variances of the individual random variables X1 through X4 respectively.

Step-by-step explanation:

To find the mean and variance of Y, we need to use the properties of the normal distribution. Since we have four independent and identically distributed random variables X1 through X4, each with a normal distribution N(12,8), we can consider the sum of these variables as Y.

The mean of Y is calculated by adding up the means of X1 through X4: 12 + 12 + 12 + 12 = 48.

The variance of Y is calculated by adding up the variances of X1 through X4: 8 + 8 + 8 + 8 = 32.