STAT 330 - CHAPTER 3 | GUARANTEED SUCCESS STARTS
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Front Answer: Back
Q: What is a random variable (RV)? Answer: A function that assigns a numerical value to each
outcome of an experiment.
Q: What is a discrete random variable? Answer: A random variable that takes on finite or
countably infinite values.
Q: What is a continuous random variable? Answer: A random variable that can take any value in
a continuous interval.
Q: What is a probability mass function (pmf)? Answer: f(x) = P(X = x), defines probabilities for a
discrete random variable.
Q: What two conditions must a pmf satisfy? Answer: "1) f(x) ≥ 0 for all x, 2) Σ f(x) = 1."
Q: What is the cumulative distribution function (cdf) for a discrete variable? Answer: F(x) = P(X ≤
x) = Σ f(t) for t ≤ x.
Q: What is the relationship between pmf and cdf? Answer: The cdf is the cumulative sum of the
pmf values.
Q: What is a probability density function (pdf)? Answer: A function for continuous random
variables where f(x) ≥ 0 and ∫ f(x) dx = 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 cdf for a continuous random variable? Answer: F(x) = ∫ from -∞ to x f(t) dt.
Q: How are pdf and cdf related? Answer: The derivative of the cdf is the pdf (for continuous
RVs).
Q: What is the expected value of a discrete random variable? Answer: E(X) = Σ x f(x).
Q: What is the expected value of a continuous random variable? Answer: E(X) = ∫ x f(x) dx.
Q: What is the variance of X? Answer: Var(X) = E[(X - μ)²] = E(X²) - μ².
Q: What is standard deviation? Answer: The square root of variance, σ = √Var(X).
Q: What is a joint probability distribution? Answer: The distribution of two or more random
variables together.
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HERE! LEARN, PRACTICE & EXCEL!
Front Answer: Back
Q: What is a random variable (RV)? Answer: A function that assigns a numerical value to each
outcome of an experiment.
Q: What is a discrete random variable? Answer: A random variable that takes on finite or
countably infinite values.
Q: What is a continuous random variable? Answer: A random variable that can take any value in
a continuous interval.
Q: What is a probability mass function (pmf)? Answer: f(x) = P(X = x), defines probabilities for a
discrete random variable.
Q: What two conditions must a pmf satisfy? Answer: "1) f(x) ≥ 0 for all x, 2) Σ f(x) = 1."
Q: What is the cumulative distribution function (cdf) for a discrete variable? Answer: F(x) = P(X ≤
x) = Σ f(t) for t ≤ x.
Q: What is the relationship between pmf and cdf? Answer: The cdf is the cumulative sum of the
pmf values.
Q: What is a probability density function (pdf)? Answer: A function for continuous random
variables where f(x) ≥ 0 and ∫ f(x) dx = 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 cdf for a continuous random variable? Answer: F(x) = ∫ from -∞ to x f(t) dt.
Q: How are pdf and cdf related? Answer: The derivative of the cdf is the pdf (for continuous
RVs).
Q: What is the expected value of a discrete random variable? Answer: E(X) = Σ x f(x).
Q: What is the expected value of a continuous random variable? Answer: E(X) = ∫ x f(x) dx.
Q: What is the variance of X? Answer: Var(X) = E[(X - μ)²] = E(X²) - μ².
Q: What is standard deviation? Answer: The square root of variance, σ = √Var(X).
Q: What is a joint probability distribution? Answer: The distribution of two or more random
variables together.
APPHIA – Crafted with Care and Precision for Academic Excellence.
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