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Q: What is a continuous random variable? Answer: A variable that can take any value in a
continuous interval.
Q: What is a probability density function (pdf)? Answer: Function f(x) ≥ 0 with total area under
curve = 1.
Q: How do you compute probabilities from a pdf? Answer: P(a < X < b) = ∫ from a to b f(x) dx.
Q: What is the cumulative distribution function (cdf)? Answer: F(x) = P(X ≤ x) = ∫ from -∞ to x
f(t) dt.
Q: What is the expected value of a continuous RV? Answer: E(X) = ∫ x f(x) dx.
Q: What is the variance of a continuous RV? Answer: Var(X) = ∫ (x-μ)² f(x) dx.
Q: What is the uniform distribution? Answer: Distribution with constant probability over [a,b].
Q: What is the pdf of a uniform distribution? Answer: f(x) = 1/(b-a) for a ≤ x ≤ b, 0 otherwise.
Q: What is the mean of a uniform distribution? Answer: μ = (a+b)/2.
Q: What is the variance of a uniform distribution? Answer: σ² = (b-a)²/12.
Q: What is the normal distribution? Answer: A bell-shaped distribution defined by mean μ and
variance σ².
Q: What is the pdf of the normal distribution? Answer: f(x) = (1/(σ√(2π))) e^(-(x-μ)²/(2σ²)).
Q: What are the parameters of a normal distribution? Answer: μ (mean), σ² (variance).
Q: What is the standard normal distribution? Answer: Normal distribution with μ=0 and σ²=1.
Q: How do you standardize a normal variable? Answer: Z = (X-μ)/σ.
Q: What is the 68-95-99.7 rule? Answer: Approx. 68% within 1σ, 95% within 2σ, 99.7% within
3σ.
Q: What is the exponential distribution? Answer: Models waiting time between events in a
Poisson process.
Q: What is the pdf of an exponential distribution? Answer: f(x) = λ e^(-λx), x ≥ 0.
Q: What is the mean of an exponential distribution? Answer: μ = 1/λ.
Q: What is the variance of an exponential distribution? Answer: σ² = 1/λ².
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HERE! LEARN, PRACTICE & EXCEL!
Q: What is a continuous random variable? Answer: A variable that can take any value in a
continuous interval.
Q: What is a probability density function (pdf)? Answer: Function f(x) ≥ 0 with total area under
curve = 1.
Q: How do you compute probabilities from a pdf? Answer: P(a < X < b) = ∫ from a to b f(x) dx.
Q: What is the cumulative distribution function (cdf)? Answer: F(x) = P(X ≤ x) = ∫ from -∞ to x
f(t) dt.
Q: What is the expected value of a continuous RV? Answer: E(X) = ∫ x f(x) dx.
Q: What is the variance of a continuous RV? Answer: Var(X) = ∫ (x-μ)² f(x) dx.
Q: What is the uniform distribution? Answer: Distribution with constant probability over [a,b].
Q: What is the pdf of a uniform distribution? Answer: f(x) = 1/(b-a) for a ≤ x ≤ b, 0 otherwise.
Q: What is the mean of a uniform distribution? Answer: μ = (a+b)/2.
Q: What is the variance of a uniform distribution? Answer: σ² = (b-a)²/12.
Q: What is the normal distribution? Answer: A bell-shaped distribution defined by mean μ and
variance σ².
Q: What is the pdf of the normal distribution? Answer: f(x) = (1/(σ√(2π))) e^(-(x-μ)²/(2σ²)).
Q: What are the parameters of a normal distribution? Answer: μ (mean), σ² (variance).
Q: What is the standard normal distribution? Answer: Normal distribution with μ=0 and σ²=1.
Q: How do you standardize a normal variable? Answer: Z = (X-μ)/σ.
Q: What is the 68-95-99.7 rule? Answer: Approx. 68% within 1σ, 95% within 2σ, 99.7% within
3σ.
Q: What is the exponential distribution? Answer: Models waiting time between events in a
Poisson process.
Q: What is the pdf of an exponential distribution? Answer: f(x) = λ e^(-λx), x ≥ 0.
Q: What is the mean of an exponential distribution? Answer: μ = 1/λ.
Q: What is the variance of an exponential distribution? Answer: σ² = 1/λ².
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