6. Probability and Statistics

Continuous Distributions — Quiz

Test your understanding of continuous distributions with 5 practice questions.

Practice Questions

Question 1

Suppose X is uniformly distributed on [0,4] and Y=2X+3. What is the probability density function f_Y(y)?

Question 2

What is the moment-generating function M_X(t) of a normal random variable X ∼ N(μ,σ^2)?

Question 3

For a gamma distribution with shape parameter k and scale parameter θ, what is the variance Var(X)?

Question 4

Let X be a continuous random variable with pdf f_X(x). If Y=h(X) where h is strictly increasing and differentiable, what is the pdf f_Y(y)?

Question 5

What is the mgf M_X(t) of a continuous uniform random variable X ∼ U(a,b)?