Binomial and Geometric Distribution

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What is the Binomial Distribution?

Back

A probability distribution that summarizes the likelihood that a value will take one of two independent states and is defined by the number of trials (n) and the probability of success (p).

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What are the assumptions of the Binomial Distribution?

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1. Fixed number of trials (n). 2. Each trial is independent. 3. Each trial has only two outcomes (success or failure). 4. The probability of success (p) is constant for each trial.

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What is the formula for the Binomial Probability?

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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.

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What is a Geometric Distribution?

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A probability distribution that models the number of trials needed to get the first success in a series of independent Bernoulli trials.

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What is the formula for the Geometric Probability?

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P(X=k) = (1-p)^(k-1) * p, where k is the number of trials until the first success and p is the probability of success.

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What is the difference between Binomial and Geometric Distribution?

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Binomial distribution counts the number of successes in a fixed number of trials, while Geometric distribution counts the number of trials until the first success.

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What does P(X≥k) represent?

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The probability that the random variable X is greater than or equal to k.

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What does P(X

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The probability that the random variable X is less than k.

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What does P(a

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The probability that the random variable X falls between a and b, exclusive.

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What is a discrete random variable?

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A random variable that can take on a countable number of values, such as the number of successes in a series of trials.