Discrete Random Variables

Question 1

What is a random variable?

Answer 1

A variable whose value is subject to variations due to chance. It can take a set of possible different values each with an associated probability.

Question 2

Discrete vs continuous

Answer 2

Only a set number of obtainable values compared to continuous.

Question 3

Properties of a valid probability distribution

Answer 3

All probabilities must be greater than or equal to 0

The sum of all probabilities must be equal to 1

Question 4

Expectation of a random variable

Answer 4

Analogous to the mean

Sum of P(X=x) multiplied by x

Question 5

Variance formula

Answer 5

E(X^2) - (E(X))^2

Question 6

Expectation of X formula

Answer 6

1/2 n(n+1)

Question 7

E(ax+b)=?

Answer 7

aE(X) + b

Question 8

Variance of aX + b

Answer 8

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

Question 9

If X and Y are two random variables, what is their expectation and variance?

Answer 9

• E(X+Y) = E(X) + E(Y)
• E(X-Y) = E(X) - E(Y)
• Var(X + or - Y) = Var(X) + Var(Y)

Question 10

E(aX+bY)=?

Answer 10

aE(X) + bE(Y)

Question 11

A random variable Y is said to be dependent on X if…

Answer 11

• the outcome of X affects the probability distribution of Y

Question 12

Two random variables are independent if…

Answer 12

• the outcome of one variable does not affect the probability distribution of the other

Question 13

If X and Y are independent events, go through the variance of X+Y

Answer 13

Var(X±Y) = var(X) + var(Y) ALWAYS PLUS
Var(aX±bY) = a^2var(X) + b^2var(Y)

E.g. var(2X) = 2^2var(X)
Var (X1+X2) = 2var(X) since X is distributed exactly the same