Discrete Probability & Expected Values

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What is a discrete probability distribution?

Back

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.

Front

Define expected value in probability.

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 of occurrence.

Front

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

Back

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

Front

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

Back

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?

Back

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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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.

Front

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?

Back

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

Front

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

Back

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?

Back

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.