Expected Value and Binomial Distribution

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What is Expected Value?

Back

Expected Value is the average outcome of a random event, calculated by multiplying each possible outcome by its probability and summing the results.

Tags

CCSS.HSS.MD.A.2

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How do you calculate Expected Value for a coin flip?

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Multiply the value of each outcome by its probability: (0.5 * $4) + (0.5 * -$3) = $0.50.

Tags

CCSS.HSS.MD.A.2

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What does a negative Expected Value indicate?

Back

A negative Expected Value indicates that, on average, you are expected to lose money over time.

Tags

CCSS.HSS.MD.B.5B

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What is a Binomial Distribution?

Back

A Binomial Distribution models the number of successes in a fixed number of independent trials, each with the same probability of success.

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What are the parameters of a Binomial Distribution?

Back

The parameters are n (number of trials) and p (probability of success on each trial).

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

How do you find 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).

Tags

CCSS.HSS.MD.A.4

CCSS.HSS.MD.A.3

Front

What is the formula for calculating combinations (n choose k)?

Back

The formula is n! / (k! * (n-k)!), where n is the total number of items, and k is the number of items to choose.

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What is the probability of getting at most k successes in a Binomial Distribution?

Back

Sum the probabilities of getting 0 to k successes: P(X ≤ k) = Σ P(X = i) for i = 0 to k.

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How do you interpret the results of a Binomial Distribution?

Back

The results indicate the likelihood of a certain number of successes occurring in a given number of trials.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

What is the expected value of a Binomial Distribution?

Back

The expected value is calculated as E(X) = n * p, where n is the number of trials and p is the probability of success.

Tags

CCSS.HSS.MD.A.2