BMath Bachelor of Mathematics Probability and Statistics

Question 1

If P(A) = 0.4, P(B) = 0.5, and A and B are independent, what is P(A ∩ B)?

Accepted Answer

0.2

Answer

For independent events, P(A ∩ B) = P(A)·P(B) = 0.4 × 0.5 = 0.2.

Question 2

What does the expected value E[X] of a discrete random variable X represent?

Accepted Answer

The weighted average of all possible values

Answer

E[X] = Σ x·P(X = x) is the long-run average value of X over many repetitions of the experiment.

Question 3

Which distribution models the number of successes in n independent Bernoulli trials with probability p?

Accepted Answer

Binomial distribution

Answer

The Binomial distribution B(n, p) counts successes in n independent trials, each with success probability p.

Question 4

Bayes' Theorem states that P(A|B) equals:

Accepted Answer

P(A)·P(B|A) / P(B)

Answer

Bayes' Theorem: P(A|B) = P(B|A)·P(A) / P(B), allowing us to update probabilities based on new evidence.

Question 5

The variance Var(X) of a random variable X is defined as:

Accepted Answer

E[(X − E[X])²]

Answer

Variance measures the expected squared deviation from the mean: Var(X) = E[(X − μ)²] = E[X²] − μ².

BMath Bachelor of Mathematics Practice Test