# confidence interval question

I need some hints for the following questions.

Let $X_1, \dots, X_8$ be a random sample from a normal population having known mean $\mu$ and variance 2. Let $\bar X_7={1\over 7} \sum_1^7X_i$ be the average of the first 7 of them.

1. What is the mean and variance of $X_8-\bar X_7$?

2. If $\bar X_7=4$, give an interval that will contain the value of $X_8$ with 95% confidence.

## 1 Answer

Some hints which might help you do the calculations:

• The expected value of the sum of random variables is the sum of their expected values

• The expected value of the difference of random variables is the difference of their expected values

• The expected value of the mean of random variables is the mean of their expected values

• The variance of the sum of independent random variables is the sum of their variances

• The variance of the difference of independent random variables is the sum of their variances

• The variance of the mean of independent random variables is the sum of their variances divided by the square of the number of random variables

• I can`t caluating course. please show me. – user72446 Dec 10 '12 at 9:07