STT 441 FINAL EXAM QUESTIONS AND ANSWERS
Binomial Distribution (Bin(n, p)) - CORRECT ANSWER✅✅Use When: You have a fixed number of
independent trials (n), each with the same probability of success (p).
Example: Flipping a coin 10 times (n = 10) and counting the number of heads, assuming the probability
of getting heads (p) is 0.5.
Geometric Distribution (Geom(p)) - CORRECT ANSWER✅✅Use When: You're counting the number of
trials until the first success in a series of independent trials, each with the same probability of success
(p).
Example: Rolling a die until you get a 6, where the probability of getting a 6 (p) is 1/6.
Negative Binomial Distribution (NBin(r, p)) - CORRECT ANSWER✅✅Use When: Similar to the geometric
distribution, but you're counting the number of trials until the r-th success.
Example: Tossing a coin until you get 3 heads, with each toss having a 0.5 chance of being heads.
Poisson Distribution (Poisson(λ)) - CORRECT ANSWER✅✅Use When: Modeling the number of times an
event happens in a fixed interval of time or space, when these events occur with a known constant
mean rate (λ) and independently of the time since the last event.
Example: Counting the number of cars passing a checkpoint on a road in an hour, assuming the cars pass
independently and at a constant average rate.
Uniform Distribution (Unif(a, b)) - CORRECT ANSWER✅✅Use When: Each outcome in a range (from a to
b) is equally likely.
Example: Rolling a fair die, where each outcome from 1 to 6 is equally likely.
Normal Distribution (N(µ, σ²)) - CORRECT ANSWER✅✅Use When: Modeling continuous data where the
distribution's shape is symmetric and bell-shaped, centered around the mean (µ), with spread
determined by the standard deviation (σ).
Example: Measuring the heights of adult men in a large population, where the heights are normally
distributed with a certain mean (µ) and standard deviation (σ).
Exponential Distribution (Exp(λ)) - CORRECT ANSWER✅✅Use When: Modeling the time between events
in a Poisson process, where events occur continuously and independently at a constant average rate (λ).
Binomial Distribution (Bin(n, p)) - CORRECT ANSWER✅✅Use When: You have a fixed number of
independent trials (n), each with the same probability of success (p).
Example: Flipping a coin 10 times (n = 10) and counting the number of heads, assuming the probability
of getting heads (p) is 0.5.
Geometric Distribution (Geom(p)) - CORRECT ANSWER✅✅Use When: You're counting the number of
trials until the first success in a series of independent trials, each with the same probability of success
(p).
Example: Rolling a die until you get a 6, where the probability of getting a 6 (p) is 1/6.
Negative Binomial Distribution (NBin(r, p)) - CORRECT ANSWER✅✅Use When: Similar to the geometric
distribution, but you're counting the number of trials until the r-th success.
Example: Tossing a coin until you get 3 heads, with each toss having a 0.5 chance of being heads.
Poisson Distribution (Poisson(λ)) - CORRECT ANSWER✅✅Use When: Modeling the number of times an
event happens in a fixed interval of time or space, when these events occur with a known constant
mean rate (λ) and independently of the time since the last event.
Example: Counting the number of cars passing a checkpoint on a road in an hour, assuming the cars pass
independently and at a constant average rate.
Uniform Distribution (Unif(a, b)) - CORRECT ANSWER✅✅Use When: Each outcome in a range (from a to
b) is equally likely.
Example: Rolling a fair die, where each outcome from 1 to 6 is equally likely.
Normal Distribution (N(µ, σ²)) - CORRECT ANSWER✅✅Use When: Modeling continuous data where the
distribution's shape is symmetric and bell-shaped, centered around the mean (µ), with spread
determined by the standard deviation (σ).
Example: Measuring the heights of adult men in a large population, where the heights are normally
distributed with a certain mean (µ) and standard deviation (σ).
Exponential Distribution (Exp(λ)) - CORRECT ANSWER✅✅Use When: Modeling the time between events
in a Poisson process, where events occur continuously and independently at a constant average rate (λ).
