PMF Expected Value and Variance of PMFs

Question 1

How is the expected value E[X] of a discrete random variable X computed from its PMF?

Accepted Answer

E[X] = Σ x × P(X=x) over all x

Answer

E[X] = Σ P(X=x) over all x

Answer

E[X] = max{P(X=x)}

Answer

E[X] = Σ x² × P(X=x) over all x

Question 2

For a fair six-sided die, what is E[X]?

Accepted Answer

3.5

Answer

3

Answer

4

Answer

21

Question 3

How is Var(X) computed from a PMF?

Accepted Answer

Var(X) = E[X²] - (E[X])²

Answer

Var(X) = E[X] - (E[X²])

Answer

Var(X) = Σ x² × P(X=x)

Answer

Var(X) = E[(X + E[X])²]

Question 4

If E[X] = 4 and E[X²] = 20, what is Var(X)?

Accepted Answer

4

Answer

16

Answer

24

Answer

80

Question 5

What is the standard deviation of X if Var(X) = 9?

Accepted Answer

3

Answer

9

Answer

81

Answer

4.5

Question 6

For the PMF P(X=1) = 0.4 and P(X=3) = 0.6, what is E[X]?

Accepted Answer

2.2

Answer

2

Answer

1.8

Answer

4