Discrete Probability & Expected Values

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What is a discrete probability distribution?

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A discrete probability distribution is a statistical distribution that describes the likelihood of outcomes of a discrete random variable, where the variable can take on a countable number of values.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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Define expected value in probability.

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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 of occurrence.

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CCSS.HSS.MD.A.2

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

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To calculate the expected value, multiply each possible value of the random variable by its probability and sum all these products.

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CCSS.HSS.MD.A.2

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What is the formula for calculating the probability of getting at least k successes in a binomial distribution?

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P(X >= k) = 1 - P(X < k) = 1 - Σ[P(X = i)] for i = 0 to k-1.

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What does it mean for a distribution to be a probability distribution?

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A probability distribution must satisfy two conditions: all probabilities must be between 0 and 1, and the sum of all probabilities must equal 1.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What is the mean of a probability distribution?

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The mean of a probability distribution is the expected value, representing the average outcome of a random variable.

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If a household has a 30% chance of having 1 child, a 43% chance of having 2 children, and a 27% chance of having 3 children, how do you find the expected number of children?

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Multiply each number of children by its probability: (1*0.30) + (2*0.43) + (3*0.27) = 1.97.

Tags

CCSS.HSS.MD.A.2

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What is the probability of guessing exactly 4 out of 5 questions correctly on a true-false quiz?

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Use the binomial probability formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k). For k=4, n=5, p=0.5, it equals 0.1875.

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What is a binomial experiment?

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A binomial experiment is a statistical experiment that has the following properties: a fixed number of trials, two possible outcomes (success or failure), constant probability of success, and independent trials.

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What is the difference between a discrete and continuous random variable?

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A discrete random variable can take on a countable number of values, while a continuous random variable can take on an infinite number of values within a given range.