Normal Distribution

Question 1

What are the parameters of the normal distribution?

Answer 1

Mean and variance

Question 2

What is the relationship between variance and standard deviation?

Answer 2

Standard deviation squared=variance.

Question 3

How do you standardise a normal distribution?

Answer 3

z=x-mu/sigma Z-N(0,1)

Question 4

How do you combine two normal random variables and their expectations?

Answer 4

As long as the two observations are independant you can just add the 2 observations and the resulting distribution is normal.The expectations are added .

Question 5

How do you combine the variances for the two independant observations?

Answer 5

You use the standard variance results as long as the observations are independant.

Question 6

What does phi represent?

Answer 6

The cdf of the standardised normal distribution

Question 7

What happens when you use a linear transformation on a normal variable?

Answer 7

The result is a normal random variable and same linear transformation rules apply.

Question 8

What distribution does multiple normal observations follow?

Answer 8

They follow the normal distribution.

Question 9

When is a sample mean used?

Answer 9

It is used to find a better estimate of the population mean.

Question 10

What are the 2 conditions for the parent distribution of a sample mean distribution?

Answer 10

If the parent distribution is normal the resulting sample mean distribution is normal.
The CLT for a large sample size N the distribution of the sample means is normal no matter what the parent distribution was.N>25