Maths & Stats Review and Descriptive Statistics

Question 1

What is a random variable?

Answer 1

A variable that can take on any value from a
given set, and value is at least in part determined by chance.

Question 2

What are three types of random variables?

Answer 2

Bernoulli (binary) - only values of 0 and 1
Discrete - a finite number of values
Continuous - infinitely many values

Question 3

What is a PDF?

Answer 3

Probability Distribution Function
The diagram showing the probability of each possible score

Question 4

How do we call the diagram that shows the probability of each possible score when there are infinite outcomes?

Answer 4

Probability Density Function

Question 4

What happens to the random variable when we increase the number of outcomes to infinity?

Answer 4

The discrete random variable becomes a continuous random variable.

Question 5

When we are interested in the probability that a random variable is below a certain value, what diagram can we use?

Answer 5

Cumulative Distribution Function (S-Shape)

Question 6

When we want to know a distribution of two discrete random variables, what will we use?

Answer 6

Joint distribution is described by Joint PDF.

Question 7

When are two variables independent?

Answer 7

When knowing the outcome of X doesn’t change the probabilities of the possible outcomes of Y.

Question 8

When two variables are dependent on each other, how can we measure their relationship?

Answer 8

Conditional distribution described by conditional PDF

Question 9

What are three measures of Central Tendency?

Answer 9

Expected Value
Mean
Median

Question 10

What are two measures of dispersion?

Answer 10

Variance and standard deviation

Question 11

Describe the variance.

Answer 11

How far a random variable deviates from the mean.

Question 12

What are two measures of association?

Answer 12

Covariance and correlation

Question 13

Describe the covariance.

Answer 13

Covariance is a measure of how two variables change together. If both variables tend to increase or decrease simultaneously, the covariance is positive. If one increases while the other decreases, it’s negative. Covariance indicates the direction of the relationship but not its strength or scale.

Question 14

Describe the correlation.

Answer 14

Correlation measures the strength and direction of the relationship between two variables. It standardizes covariance, giving a value between -1 and 1. A value of 1 indicates a perfect positive relationship, -1 indicates a perfect negative relationship, and 0 means no linear relationship.

Question 15

What is the difference between mean and median.

Answer 15

The mean is the average of all data points, calculated by summing the values and dividing by the number of points. The median is the middle value in a dataset when it is ordered from least to greatest. The key difference is that the mean is affected by outliers, while the median is more robust to extreme values.

Question 16

Describe a normal distribution

Answer 16

A normal distribution is a symmetric, bell-shaped probability distribution where most values cluster around the mean. In this distribution, the mean, median, and mode are equal, and data is evenly distributed on both sides. It is defined by two parameters: the mean (center) and standard deviation (spread). Many natural phenomena follow a normal distribution.

Question 17

What is a standard normal distribution?

Answer 17

A normal distribution with mean = 0 and standard deviation = 1.