# Normal Distribution

1. Oct 3, 2007

### steven10137

1. The problem statement, all variables and given/known data
x represents values of a Normal random variable X, with parameters $$\mu$$ and $$\sigma^2$$
z represents corresponding values of normal random variable Z, with parameters 0 and 1.

z x
-3 22
-2 34.5
1 72
3 97

The following questions relate to the tabled data:
a) calculate the correlation co-efficient between z and x.
b) calculate the regression equation used to predict x if z is unknown
c) determine the values of $$\mu$$ and $$\sigma^2$$

2. The attempt at a solution
Well the random variable Z has a mean 0 and variance 1, meaning that it is a standard normal distribution.

a) can I just use a linear regression on the data? this gives a correlation co-efficient of 1
b) using the same regression, x=12.5z+59.5 ??
c) Now im stuck.

Cheers
Steven
(sorry I have exams coming up ... hence the rush of posts)

Last edited: Oct 3, 2007
2. Oct 3, 2007

### EnumaElish

"used to predict x if z is unknown" doesn't make sense. You have to know at least one.

For correlation I wouldn't estimate the regression; just the simple correlation between x and z.

Independent of 1 and 2, what do you think the answer to 3 might be?

3. Oct 4, 2007

### steven10137

it cant be as simple as:
$$\mu=0$$
and
$$\sigma^2=1$$

can it?

4. Oct 4, 2007

### steven10137

damn just realised:

part b should be:
"calculate the regression used to predict x if z is known"

sorry

5. Oct 4, 2007

### steven10137

dont worry finally got it:
$$\mu=59.5$$
and
$$\sigma=12.5$$

thanks