Binomial Distribution

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What is a Binomial Distribution?

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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).

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What are the assumptions of a Binomial Distribution?

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

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What does P(X > k) represent in a Binomial Distribution?

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P(X > k) represents the probability of getting more than k successes in n trials.

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What does P(X < k) represent in a Binomial Distribution?

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P(X < k) represents the probability of getting fewer than k successes in n trials.

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What does P(X = k) represent in a Binomial Distribution?

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P(X = k) represents the probability of getting exactly k successes in n trials.

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How do you calculate the probability of exactly k successes in a Binomial Distribution?

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The probability is calculated using the formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where (n choose k) = n! / (k!(n-k)!).

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What is the formula for calculating the mean of a Binomial Distribution?

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The mean (μ) of a Binomial Distribution is calculated as μ = n * p.

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What is the formula for calculating the variance of a Binomial Distribution?

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The variance (σ²) of a Binomial Distribution is calculated as σ² = n * p * (1 - p).

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If a coin is flipped 10 times, what is the probability of getting exactly 5 heads?

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Using the Binomial formula: P(X = 5) = (10 choose 5) * (0.5)^5 * (0.5)^(10-5) = 0.246.

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What is the significance of the 'n' in a Binomial Distribution?

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The 'n' represents the number of trials or experiments conducted.