Probability Distributions

Front

What is a probability distribution?

Back

A probability distribution is a mathematical function that describes the likelihood of obtaining the possible values that a random variable can take.

Front

Define a binomial distribution.

Back

A binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

Front

What is the formula for the standard deviation of a binomial distribution?

Back

The standard deviation (σ) of a binomial distribution is calculated using the formula: σ = √(n * p * (1 - p)), where n is the number of trials and p is the probability of success.

Front

What is the difference between discrete and continuous random variables?

Back

Discrete random variables can take on a countable number of values, while continuous random variables can take on an infinite number of values within a given range.

Front

Give an example of a discrete random variable.

Back

The number of heads obtained when flipping a coin three times is a discrete random variable.

Front

Give an example of a continuous random variable.

Back

The height of students in a classroom is a continuous random variable.

Front

What is the probability of rolling doubles with two dice?

Back

The probability of rolling doubles with two dice is 1/6.

Front

How do you calculate the probability of getting exactly k successes in n trials in a binomial distribution?

Back

Use the formula: P(X = k) = (n choose k) * p^k * (1 - p)^(n - k), where 'n choose k' is the binomial coefficient.

Front

What is the binomial coefficient?

Back

The binomial coefficient, denoted as (n choose k), is calculated as n! / (k! * (n - k)!), where n is the total number of trials and k is the number of successes.

Front

What is the expected value of a binomial distribution?

Back

The expected value (mean) of a binomial distribution is calculated using the formula: E(X) = n * p.