Discrete random variables

Question 1

What is a random variable?

Answer 1

A variable that is the outcome of an experiment

Question 2

How is a random variable notated?

Answer 2

An uppercase letter

Question 3

How is a particular value of a random variable notated?

Answer 3

A lowercase letter

Question 4

What is a probability function?

Answer 4

A function that links each value of a random variable to its probability

Question 5

What does the cumulative distribution function do?

Answer 5

It gives the probability that a random variable X is equal to or less than a specific value

Question 6

How is the cumulative distribution function notated?

Answer 6

F(x)

Question 7

How is the expected value of a random variable X notated?

Answer 7

E(X)

Question 8

How can E(Xⁿ) be calculated?

Answer 8

Σ(xⁿ*P(X=x))

Question 9

How is the variance of a random variable notated?

Answer 9

Var(X)

Question 10

How can the variance of a random variable be calculated?

Answer 10

E(X²)-E(X)²

Question 11

What is E(aX+b) equal to?

Answer 11

aE(X)+b

Question 12

What is Var(aX+b) equal to?

Answer 12

a²Var(X)

Question 13

What is interpolation?

Answer 13

The estimation of a value of a dependent variable within the range of the data

Question 14

What is extrapolation?

Answer 14

The estimation of a value of a dependent variable outside the range of the data

Question 15

What is a discrete uniform distribution?

Answer 15

A distribution in which each value has the same probability

Question 16

For a discrete uniform distribution over the values 1,2,3,…,n, how can E(X) be calculated?

Answer 16

(n+1)/2

Question 17

For a discrete uniform distribution over the values 1,2,3,…,n, how can Var(X) be calculated?

Answer 17

(n+1)(n-1)/12