Binomial Distribution (Calculating)
Flashcard
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a Binomial Distribution?
Back
A Binomial Distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent states and is defined by two parameters: n (number of trials) and p (probability of success).
2.
FLASHCARD QUESTION
Front
What are the parameters of a Binomial Distribution?
Back
The parameters are n (the number of trials) and p (the probability of success on each trial).
3.
FLASHCARD QUESTION
Front
What does X ~ B(n, p) represent?
Back
It represents a random variable X that follows a Binomial Distribution with n trials and probability p of success.
4.
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).
5.
FLASHCARD QUESTION
Front
What is the formula for calculating P(X ≥ k) in a Binomial Distribution?
Back
P(X ≥ k) = 1 - P(X < k) = 1 - Σ P(X = i) for i = 0 to k-1.
6.
FLASHCARD QUESTION
Front
What is the cumulative distribution function (CDF) in the context of Binomial Distribution?
Back
The CDF gives the probability that the random variable X is less than or equal to a certain value k, denoted as P(X ≤ k).
7.
FLASHCARD QUESTION
Front
What is the mean of a Binomial Distribution?
Back
The mean (expected value) is calculated as E(X) = n * p.
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