6.3 Geometric vs. Binomial

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What is a Geometric Random Variable?

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A Geometric Random Variable counts the number of trials needed to obtain the first success. It can take values X = 1, 2, 3, ...

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What is a Binomial Random Variable?

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A Binomial Random Variable counts the number of successes in a fixed number of trials. It can take values X = 0, 1, 2, ..., n.

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What is the probability of success in a Geometric distribution?

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The probability of success in a Geometric distribution is constant for each trial.

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What is the probability of success in a Binomial distribution?

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The probability of success in a Binomial distribution is constant for each trial and is defined for a fixed number of trials.

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In a Geometric distribution, what does 'success' refer to?

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In a Geometric distribution, 'success' refers to the event of interest occurring, such as a user upgrading an app.

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In a Binomial distribution, what does 'success' refer to?

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In a Binomial distribution, 'success' refers to the event of interest occurring, such as winning a coupon.

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What is the formula for the probability mass function of a Geometric distribution?

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P(X = k) = (1-p)^(k-1) * p, where p is the probability of success.

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What is the formula for the probability mass function of a Binomial distribution?

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

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What is the expected value of a Geometric Random Variable?

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The expected value E(X) of a Geometric Random Variable is 1/p, where p is the probability of success.

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What is the expected value of a Binomial Random Variable?

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The expected value E(X) of a Binomial Random Variable is n*p, where n is the number of trials and p is the probability of success.