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

0.9

Answer

0.1

Answer

0.45

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

The most likely outcome

Answer

The median of the distribution

Answer

The variance of X

Question 3

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

Accepted Answer

Binomial distribution

Answer

Poisson distribution

Answer

Normal distribution

Answer

Exponential distribution

Question 4

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

Accepted Answer

P(A)·P(B|A) / P(B)

Answer

P(B|A) / P(A)

Answer

P(A ∩ B) / P(A)

Answer

P(B) / P(A|B)

Question 5

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

Accepted Answer

E[(X − E[X])²]

Answer

E[X²]

Answer

E[X]²

Answer

E[X] − E[X²]

Question 6

The Central Limit Theorem states that as n → ∞, the sample mean X̄ of i.i.d. random variables approaches:

Accepted Answer

A normal distribution regardless of the population's distribution

Answer

The median of the population

Answer

The population standard deviation

Answer

A uniform distribution