Discrete Random Variables

Question 1

What is a random variable?

Answer 1

The value of a variable that is the outcome of an experiment.

Question 2

What is the difference between X and x

Answer 2

X are used for the random variable and x is a particular value of the random variable X

Question 3

What is another way of writing P(X=x)?

Answer 3

p(x)

Question 4

What does P(X=x) refer to?

Answer 4

The probability that X is equal to a particular value x.

Question 5

What is a continuous random variable?

Answer 5

A variable where the outcome can be any value on a continuous scale.

Question 6

What is a discrete random variable?

Answer 6

A variable that only takes values on a discrete scale.

Question 7

What does a probability distribution table show?

Answer 7

The probability of each outcome of an experiment.

Question 8

What is the symbol for a cumulative distribution function?

Answer 8

F(x) = P(X=x)

Question 9

What is E(aX+b) equal to?

Answer 9

E(aX+b) = aE(X)+b

Where a and b are constants

Question 10

What is Var(aX+b) equal to?

Answer 10

Var(aX+b) = a^2 x Var(X)

Question 11

What is Var(X) equal to?

Answer 11

Var(X) = E(X^2) - [ E(X) ]^2

Question 12

What is a discrete uniform distribution?

Answer 12

Where all the probabilities are uniform (the same) and the values are discrete.

Question 13

How can the expected value and variance for a discrete uniform distribution be calculated?

Answer 13

E(X) = (n+1)/2

Var(X) = (n+1)(n-1)/12

Question 14

State the two conditions for a discrete uniform distribution.

Answer 14

1) each value is equally likely

2) a discrete random variable X is defined over a set of n distinct values.