AP Stats AP Stats Random Variables and Expected Value 2

Question 1

A binomial setting requires which of the following conditions?

Accepted Answer

Fixed number of trials, two outcomes, constant probability, independent trials

Answer

Binomial conditions (BINS): Binary outcomes, Independent trials, fixed Number of trials, and Same probability of success.

Question 2

For X ~ Binomial(n = 10, p = 0.3), what is P(X = 3)?

Accepted Answer

C(10,3)(0.3)³(0.7)⁷

Answer

P(X = k) = C(n,k) · pᵏ · (1−p)ⁿ⁻ᵏ, so P(X = 3) = C(10,3)(0.3)³(0.7)⁷.

Question 3

The standard deviation of a binomial random variable X ~ Binomial(n, p) is:

Accepted Answer

√[np(1−p)]

Answer

The standard deviation of a binomial distribution = √[np(1−p)], the square root of the variance.

Question 4

Which condition is required to use a geometric distribution?

Accepted Answer

Trials continue until the first success

Answer

A geometric distribution models the number of trials until the first success, with no fixed number of trials set in advance.

Question 5

If X and Y are independent random variables, what is Var(X − Y)?

Accepted Answer

Var(X) + Var(Y)

Answer

For independent variables, Var(X − Y) = Var(X) + Var(Y) because variances always add (subtracting a variable doesn't reduce spread).

AP Practice Test