Geometric vs. Binomial
Flashcard
•
Mathematics
•
10th Grade - University
•
Practice Problem
•
Hard
+4
Standards-aligned
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1.
FLASHCARD QUESTION
Front
What is a geometric distribution?
Back
A geometric distribution models the number of trials until the first success in a series of independent Bernoulli trials, where each trial has the same probability of success.
2.
FLASHCARD QUESTION
Front
What is a binomial distribution?
Back
A binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.
Tags
CCSS.HSS.MD.A.3
CCSS.HSS.MD.A.4
3.
FLASHCARD QUESTION
Front
What is the formula for the mean of a geometric distribution?
Back
The mean (expected value) of a geometric distribution is given by E(X) = 1/p, where p is the probability of success.
Tags
CCSS.HSS.MD.A.2
4.
FLASHCARD QUESTION
Front
What is the formula for the standard deviation of a geometric distribution?
Back
The standard deviation of a geometric distribution is given by SD(X) = sqrt((1-p)/p^2).
5.
FLASHCARD QUESTION
Front
What is the formula for the mean of a binomial distribution?
Back
The mean (expected value) of a binomial distribution is given by E(X) = n*p, where n is the number of trials and p is the probability of success.
Tags
CCSS.HSS.MD.A.2
6.
FLASHCARD QUESTION
Front
What is the formula for the standard deviation of a binomial distribution?
Back
The standard deviation of a binomial distribution is given by SD(X) = sqrt(n*p*(1-p)).
7.
FLASHCARD QUESTION
Front
How do you calculate the probability of exactly k successes in a binomial distribution?
Back
Use the formula P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success.
Tags
CCSS.HSS.MD.A.3
CCSS.HSS.MD.A.4
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