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Questions and Answers
What is the condition for Bernoulli trials where the probability of success and failure remains constant?
What is the probability of failure in a Bernoulli trial?
What is the number of trials in a Binomial distribution?
What is the probability of getting exactly two people alive at age 65 years in the mortality example?
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What is the characteristic of a Binomial random variable?
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What is the name of the coefficient that represents choosing r from n without considering the order?
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Study Notes
Binomial Coefficients
- Binomial coefficients are the same as nCr, representing the number of ways to choose r items from a set of n items without considering the order.
Bernoulli Trials
- A Bernoulli trial is a repeated experiment that satisfies three conditions: • Each trial has two possible outcomes: Success (S) and Failure (F) • The trials are independent • The probability of Success (and Failure) is constant for each trial
Binomial Distribution
- A Binomial Distribution is the probability distribution for the number of successes in a sequence of Bernoulli trials
- A Binomial Random Variable has: • n identical trials • Two outcomes: Success (S) and Failure (F) • Probability of Success: P(S) = p • Probability of Failure: P(F) = q = 1 – p • x is the number of Successes in n trials
Binomial Distribution Question
- Mortality example:
• Probability of a 20-year-old person being alive at 65 years: 80% (p = 0.8, q = 0.2)
• Find the probability that the number alive at 65 years will be:
- Exactly two
- At most one
- At least one • Determine the probability distribution of the number alive at 65
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Description
Test your understanding of binomial distribution, binomial coefficients, and Bernoulli trials. Determine the value of each binomial coefficient and learn about the conditions of Bernoulli trials.
