Test on Binomial Geometric Poisson Dec 10

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What is the expected value of a random variable?

Back

The expected value is the long-term average or mean of a random variable, calculated as the sum of all possible values, each multiplied by its probability.

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How do you calculate the expected value for a discrete random variable?

Back

Multiply each possible value of the random variable by its probability and sum all these products.

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.

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.

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What is a Poisson Distribution?

Back

A Poisson Distribution models the number of events occurring in a fixed interval of time or space, given a known average rate of occurrence.

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What is the mean symbol in statistics?

Back

The mean is represented by the symbol μ (mu).

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What is the probability of finding no successes in a Binomial Distribution?

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The probability of finding no successes can be calculated using the formula P(X=0) = (1-p)^n, where p is the probability of success and n is the number of trials.

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What is the formula for the expected value of a Binomial Distribution?

Back

The expected value (E) of a Binomial Distribution is given by E = n * p, where n is the number of trials and p is the probability of success.

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What is the formula for the expected value of a Poisson Distribution?

Back

The expected value (E) of a Poisson Distribution is equal to the mean (λ), which is the average number of events in the given interval.

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What is the difference between Binomial and Geometric Distributions?

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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.