What is a binomial distribution?
6.3 Flashcard Binomial and Geometric Distributions

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Mathematics
•
12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
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: the number of trials (n) and the probability of success (p).
2.
FLASHCARD QUESTION
Front
What is a geometric distribution?
Back
A geometric distribution models the number of trials needed to get the first success in a series of independent Bernoulli trials, where each trial has two possible outcomes (success or failure) and the probability of success is constant.
3.
FLASHCARD QUESTION
Front
How do you calculate the mean of a binomial distribution?
Back
The mean (expected value) of a binomial distribution is calculated using the formula: E(X) = n * p, where n is the number of trials and p is the probability of success.
4.
FLASHCARD QUESTION
Front
How do you calculate the standard deviation of a binomial distribution?
Back
The standard deviation of a binomial distribution is calculated using the formula: SD = sqrt(n * p * (1 - p)), where n is the number of trials and p is the probability of success.
5.
FLASHCARD QUESTION
Front
What does it mean if a random variable follows a binomial distribution?
Back
It means that the random variable represents the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.
6.
FLASHCARD QUESTION
Front
What does it mean if a random variable follows a geometric distribution?
Back
It means that the random variable represents the number of trials until the first success occurs in a series of independent Bernoulli trials.
7.
FLASHCARD QUESTION
Front
In a binomial distribution, what are the possible outcomes for each trial?
Back
The possible outcomes for each trial in a binomial distribution are 'success' or 'failure'.
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