AP Stats AP Stats Random Variables and Expected Value

Question 1

The expected value (mean) of a discrete random variable X is calculated as:

Accepted Answer

Σ x · P(X = x)

Answer

Σ x / n

Answer

Σ P(X = x)

Answer

max(x) − min(x)

Question 2

A fair coin is flipped 3 times. Let X = number of heads. What is E(X)?

Accepted Answer

1.5

Answer

1

Answer

2

Answer

0.5

Question 3

If X is a random variable and a and b are constants, then E(aX + b) equals:

Accepted Answer

aE(X) + b

Answer

aE(X)

Answer

E(X) + b

Answer

a²E(X) + b

Question 4

Which of the following describes a continuous random variable?

Accepted Answer

Exact time in seconds for a runner to finish a race

Answer

Number of students absent each day

Answer

Score on a 40-question multiple-choice test

Answer

Number of cars in a parking lot

Question 5

The variance of a discrete random variable X is defined as:

Accepted Answer

E[(X − μ)²]

Answer

E(X²)

Answer

E(X) − [E(X)]²

Answer

E(X) × P(X)

Question 6

If X and Y are independent random variables, then Var(X + Y) equals:

Accepted Answer

Var(X) + Var(Y)

Answer

Var(X) − Var(Y)

Answer

Var(X) × Var(Y)

Answer

[Var(X) + Var(Y)] / 2