Module 9.2: Normal Distributions

Question 1

What are the 5 key properties of a normal distribution?

Answer 1

1) It is completely described by its mean - “X is normally distributed with a mean u and variance o2”
2) Skewness = 0, meaning the normal distribution is symmetric about its mean.
3) Kurtosis = 3
4) A linear combination of normally distributed random variables is also normally distributed
5) The probabilities of outcomes further above and below the mean get smaller and smaller but do not go to zero.

Question 2

What is a multivariate distribution?

Answer 2

Specifies the probabilities associated with a group of random variables and is meaningful only when the behavior of each random variable in the group is some way dependent upon the behavior of others.

Question 3

What is the distinguishing factor between a univariate and multivariate normal distribution?

Answer 3

Correlation

Question 4

What are the three parameters that can define a multivariate normal distribution?

Answer 4

1) N means of the n series of returns
2) N variances of the N series of returns
3) .5n(n-1) pair-wise correlations

Question 5

What is a confidence interval?

Answer 5

Range of values around the expected outcome within which we expect the actual outcome to be some specified percentage of the time.

Question 6

For a normally distributed random variable, what percentage of outcomes will be within 1 standard deviation and 2 standard deviations?

Answer 6

68% for 1 standard deviations and 95% for 2 standard deviations

Question 7

What is the standard deviation # for 90% confidence interval, 95% confidence interval, and 99% confidence interval?

Answer 7

90% - X - 1.65 to X + 1.65
95% - X -1.96 to X + 1.96
99% - X -2.58 to X + 2.58

Question 8

What is the standard normal distribution?

Answer 8

A normal distribution that has been standardized so that it has a mean of zero and a standard deviation of 1.

Question 9

What is the z-value? What is standardization?

Answer 9

represents the number of standard deviations a given observation is from the population mean. Standardization is the process of converting an observed value for a random variable to its z-value.

Question 10

What is the z-value formula?

Answer 10

observation - population mean / standard deviation