BMath Bachelor of Mathematics Probability and Statistics 3

Question 1

The law of total probability states that P(B) equals:

Accepted Answer

P(B|A)·P(A) + P(B|Aᶜ)·P(Aᶜ)

Answer

P(B|A) + P(B|Aᶜ)

Answer

P(A)·P(B)

Answer

P(A ∪ B) − P(A)

Question 2

For the exponential distribution with rate λ, the mean is:

Accepted Answer

1/λ

Answer

λ

Answer

λ²

Answer

1/λ²

Question 3

In simple linear regression y = β₀ + β₁x + ε, what does β₁ represent?

Accepted Answer

The expected change in y for a one-unit increase in x

Answer

The y-intercept of the regression line

Answer

The variance of the error term

Answer

The correlation coefficient

Question 4

The p-value in a hypothesis test represents:

Accepted Answer

The probability of observing a result as extreme as the data, assuming H₀ is true

Answer

The probability that the null hypothesis is true

Answer

The probability of a Type II error

Answer

The significance level α

Question 5

For two independent random variables X and Y, Var(X + Y) equals:

Accepted Answer

Var(X) + Var(Y)

Answer

Var(X) · Var(Y)

Answer

Var(X) + Var(Y) + 2Cov(X,Y)

Answer

(Var(X) + Var(Y))²

Question 6

The geometric distribution models:

Accepted Answer

The number of trials until the first success

Answer

The number of successes in n trials

Answer

The time between events in a Poisson process

Answer

The total distance traveled in a random walk