STAT 330 - Chapter 6 Exam with
Complete Solutions
"Rule of thumb for normal distributions: 68% within 1σ, 95% within 2σ, 99.7% within 3σ."
- ANSWER-T: 68-95-99.7 Rule
1), what is P(X<0.25)?,P=0.25. - ANSWER-Q: Example: If X ~ Uniform(0
A bell-shaped distribution defined by mean μ and variance σ². - ANSWER-Q: What is
the normal distribution?
A continuous distribution generalizing exponential, defined by α (shape) and β (scale). -
ANSWER-Q: What is the gamma distribution?
A gamma distribution with α = k/2 and β = 2, where k is degrees of freedom. -
ANSWER-Q: What is the chi-square distribution?
A variable that can take any value in a continuous interval. - ANSWER-Q: What is a
continuous random variable?
Approx. 68% within 1σ, 95% within 2σ, 99.7% within 3σ. - ANSWER-Q: What is the 68-
95-99.7 rule?
Bell curve defined by μ and σ². - ANSWER-T: Normal Distribution
Distribution with constant probability over [a,b]. - ANSWER-Q: What is the uniform
distribution?
E(X) = ∫ x f(x) dx. - ANSWER-Q: What is the expected value of a continuous RV?
Equal likelihood over [a,b]. - ANSWER-T: Uniform Distribution
f(x) = (1/(Γ(α)β^α)) x^(α-1) e^(-x/β), x>0. - ANSWER-Q: What is the pdf of the gamma
distribution?
f(x) = (1/(σ√(2π))) e^(-(x-μ)²/(2σ²)). - ANSWER-Q: What is the pdf of the normal
distribution?
f(x) = 1/(b-a) for a ≤ x ≤ b, 0 otherwise. - ANSWER-Q: What is the pdf of a uniform
distribution?
Complete Solutions
"Rule of thumb for normal distributions: 68% within 1σ, 95% within 2σ, 99.7% within 3σ."
- ANSWER-T: 68-95-99.7 Rule
1), what is P(X<0.25)?,P=0.25. - ANSWER-Q: Example: If X ~ Uniform(0
A bell-shaped distribution defined by mean μ and variance σ². - ANSWER-Q: What is
the normal distribution?
A continuous distribution generalizing exponential, defined by α (shape) and β (scale). -
ANSWER-Q: What is the gamma distribution?
A gamma distribution with α = k/2 and β = 2, where k is degrees of freedom. -
ANSWER-Q: What is the chi-square distribution?
A variable that can take any value in a continuous interval. - ANSWER-Q: What is a
continuous random variable?
Approx. 68% within 1σ, 95% within 2σ, 99.7% within 3σ. - ANSWER-Q: What is the 68-
95-99.7 rule?
Bell curve defined by μ and σ². - ANSWER-T: Normal Distribution
Distribution with constant probability over [a,b]. - ANSWER-Q: What is the uniform
distribution?
E(X) = ∫ x f(x) dx. - ANSWER-Q: What is the expected value of a continuous RV?
Equal likelihood over [a,b]. - ANSWER-T: Uniform Distribution
f(x) = (1/(Γ(α)β^α)) x^(α-1) e^(-x/β), x>0. - ANSWER-Q: What is the pdf of the gamma
distribution?
f(x) = (1/(σ√(2π))) e^(-(x-μ)²/(2σ²)). - ANSWER-Q: What is the pdf of the normal
distribution?
f(x) = 1/(b-a) for a ≤ x ≤ b, 0 otherwise. - ANSWER-Q: What is the pdf of a uniform
distribution?
