Dec 4 - Discrete Probability Distributions

Front

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

What is the probability of getting exactly k successes in n independent Bernoulli trials?

Back

The probability is given by the formula P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where p is the probability of success.

Front

Define a discrete random variable.

Back

A discrete random variable is a variable that can take on a finite or countably infinite number of values, each with an associated probability.

Front

What is the expected value of a discrete random variable?

Back

The expected value is the long-term average value of repetitions of the experiment it represents, calculated as E(X) = Σ [x * P(X=x)] for all possible values x.

Front

What is the variance of a discrete random variable?

Back

Variance measures the spread of a set of values, calculated as Var(X) = E(X^2) - (E(X))^2.

Front

What is the probability of at least k successes in n trials?

Back

The probability of at least k successes is calculated as P(X ≥ k) = 1 - P(X < k) = 1 - Σ P(X = j) for j = 0 to k-1.

Front

What is a binomial distribution?

Back

A binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent Bernoulli trials.

Front

What is the formula for the binomial coefficient?

Back

The binomial coefficient is given by (n choose k) = n! / (k!(n-k)!), where n is the total number of trials and k is the number of successes.

Front

What does it mean for a variable to be 'discrete'?

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A variable is discrete if it can take on only specific, distinct values, often counts of items, such as the number of students in a class.

Front

What is the probability of guessing at least 4 correct answers on a 5-question true-false quiz?

Back

The probability is calculated using the binomial distribution formula, resulting in P(X ≥ 4) = P(X=4) + P(X=5) = 0.1875.