STAT 330 Chapter 3 Solved 100% Correct
Q: How do you compute probabilities from a pdf? - ANSWER-P(a < X < b) = ∫ from a to
b f(x) dx.
Q: How is the cumulative distribution function (cdf) for a discrete variable defined? -
ANSWER-F(x) = P(X ≤ x) = Σ f(t) for t ≤ x.
Q: What is a conditional distribution? - ANSWER-The probability distribution of one
variable given another has occurred.
Q: What is a continuous random variable? - ANSWER-A random variable that can take
any value in an interval (e.g., height, time, weight).
Q: What is a discrete random variable? - ANSWER-A random variable with countable
possible values (e.g., number of children, defects).
Q: What is a joint probability distribution? - ANSWER-The probability distribution of two
or more random variables.
Q: What is a marginal distribution? - ANSWER-The distribution of one variable obtained
by summing (discrete) or integrating (continuous) over others.
Q: What is a probability density function (pdf)? - ANSWER-A function for continuous
RVs where f(x) ≥ 0 and ∫ f(x) dx = 1.
Q: What is a random variable (RV)? - ANSWER-A function that assigns a numerical
value to each outcome of an experiment.
Q: What is the relationship between pmf and cdf? - ANSWER-The cdf is the cumulative
sum of the pmf values up to x.
Q: What two conditions must a probability mass function (pmf) satisfy? - ANSWER-1)
f(x) ≥ 0 for all x, 2) The sum of all probabilities equals 1.
T: Conditional Distribution - ANSWER-Distribution of one variable given another is fixed.
T: Continuous Random Variable - ANSWER-Takes values over an interval.
T: Cumulative Distribution Function (cdf) - ANSWER-F(x) = P(X ≤ x), cumulative
probability up to x.
T: Discrete Random Variable - ANSWER-Takes finite or countable values.
T: Independence (Random Variables) - ANSWER-Two RVs are independent if joint
pdf/pmf = product of marginals.
Q: How do you compute probabilities from a pdf? - ANSWER-P(a < X < b) = ∫ from a to
b f(x) dx.
Q: How is the cumulative distribution function (cdf) for a discrete variable defined? -
ANSWER-F(x) = P(X ≤ x) = Σ f(t) for t ≤ x.
Q: What is a conditional distribution? - ANSWER-The probability distribution of one
variable given another has occurred.
Q: What is a continuous random variable? - ANSWER-A random variable that can take
any value in an interval (e.g., height, time, weight).
Q: What is a discrete random variable? - ANSWER-A random variable with countable
possible values (e.g., number of children, defects).
Q: What is a joint probability distribution? - ANSWER-The probability distribution of two
or more random variables.
Q: What is a marginal distribution? - ANSWER-The distribution of one variable obtained
by summing (discrete) or integrating (continuous) over others.
Q: What is a probability density function (pdf)? - ANSWER-A function for continuous
RVs where f(x) ≥ 0 and ∫ f(x) dx = 1.
Q: What is a random variable (RV)? - ANSWER-A function that assigns a numerical
value to each outcome of an experiment.
Q: What is the relationship between pmf and cdf? - ANSWER-The cdf is the cumulative
sum of the pmf values up to x.
Q: What two conditions must a probability mass function (pmf) satisfy? - ANSWER-1)
f(x) ≥ 0 for all x, 2) The sum of all probabilities equals 1.
T: Conditional Distribution - ANSWER-Distribution of one variable given another is fixed.
T: Continuous Random Variable - ANSWER-Takes values over an interval.
T: Cumulative Distribution Function (cdf) - ANSWER-F(x) = P(X ≤ x), cumulative
probability up to x.
T: Discrete Random Variable - ANSWER-Takes finite or countable values.
T: Independence (Random Variables) - ANSWER-Two RVs are independent if joint
pdf/pmf = product of marginals.
