STAT 330 - Chapter 6 Exam Questions With 100% Correct Answer

Q: What is a continuous random variable?



Ans: A variable that can take any value in a continuous interval.



Quiz Q: What is a probability density function (pdf)?



Ans: Function f(x) ≥ 0 with total area under curve = 1.



Quiz Q: How do you compute probabilities from a pdf?



Ans: P(a < X < b) = ∫ from a to b f(x) dx.



Quiz Q: What is the cumulative distribution function (cdf)?



Ans: F(x) = P(X ≤ x) = ∫ from -∞ to x f(t) dt.



Quiz Q: What is the expected value of a continuous RV?

, Ans: E(X) = ∫ x f(x) dx.



Quiz Q: What is the variance of a continuous RV?



Ans: Var(X) = ∫ (x-μ)² f(x) dx.



Quiz Q: What is the uniform distribution?



Ans: Distribution with constant probability over [a,b].



Quiz Q: What is the pdf of a uniform distribution?



Ans: f(x) = 1/(b-a) for a ≤ x ≤ b, 0 otherwise.



Quiz Q: What is the mean of a uniform distribution?



Ans: μ = (a+b)/2.



Quiz Q: What is the variance of a uniform distribution?



Ans: σ² = (b-a)²/12.



Quiz Q: What is the normal distribution?



Ans: A bell-shaped distribution defined by mean μ and variance σ².