Characteristics of probability distributions

Question 1

Define: Expected Value

Answer 1

it is the sum of products of the values taken by the random variable and their corresponding probabilities.

Question 2

Define: Variance

Answer 2

Variance measures the distribution of individual values around the mean.

It is the expected value of the squared difference between an individual X value and its mean/ expected value (μ).

Question 3

Define: Standard deviation

Question 4

Define: Skewness

Answer 4

The third moment of probability distributions.

is a measure of asymmetry of a PDF.

Question 5

Skewness (S) is positive

Answer 5

the PDF is right or positively skewed

Question 6

Skewness (S) is negative

Answer 6

the PDF is left or negatively skewed.

Question 7

Define: Kurtosis

Answer 7

The fourth moment of a distribution, is a measure of the tallness of flatness of a PDF.

Question 8

K < 3

Answer 8

PDF is flat/short-tailed (

Question 9

Properties of correlation coefficient

Answer 9

Can be + or -, same sign as covariance.
Measure linear relationship.
Values between perfect + and perfect – relationship
Pure number devoid of units of measurement
Covariance zero if statistically independent; correlation also zero
Correlation does not imply causality.

Question 10

Define: Parameter

Answer 10

A summary value determined for the population

Question 11

Define: Statistic/Estimate

Answer 11

A summary value determined from a sample

Question 12

Properties of the Normal distribution

Answer 12

The normal distribution curve is symmetrical around its mean value.

The probability of obtaining a value close to the mean is higher than to obtain a value close to the tail.

68% of the values under a normal curve lies within 1 standard deviation from the mean

95% of the values under a normal curve lies within 2 standard deviation from the mean.

99% of the values under a normal curve lies within 3 standard deviation from the mean

It is possible to determine the probability that X lies within a certain interval if the mean and variance are known.

Any linear combination of two or more normally distributed random variable is itself normally distributed

A normal distribution has a skewness of 0 and kurtosis of 3.

Question 13

Properties of the t distribution

Answer 13

Symmetric
Mean is zero
Variance is k/(k-2)
T approaches standard normal distribution as df increases

Question 14

Properties X^2 distribution

Answer 14

Only positive values
Skewed; low df more skew

Question 15

Properties of the F distribution

Answer 15

Skewed
Between 0 and infinity