Binomial and Geometric Distribution

Front

What is the expected value in a probability distribution?

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.

Front

What are the assumptions of the Binomial distribution?

Back

1. Fixed number of trials 2. Each trial is independent 3. Each trial has only two outcomes (success or failure) 4. The probability of success is constant across trials.

Front

What is a discrete random variable?

Back

A discrete random variable is one that can take on a countable number of distinct values, such as the number of successes in a series of trials.

Front

What is a geometric distribution?

Back

A geometric distribution models the number of trials needed to achieve the first success in a series of independent Bernoulli trials.

Front

How do you calculate the expected value of a Binomial distribution?

Back

E(X) = n * 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 take on countable values, while continuous random variables can take on any value within a given range.

Front

What is the formula for the probability mass function of a Binomial distribution?

Back

P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success.

Front

What does it mean for trials to be independent in a Binomial distribution?

Back

It means the outcome of one trial does not affect the outcome of another trial.

Front

What is the significance of the sum of probabilities in a probability distribution?

Back

The sum of all probabilities in a probability distribution must equal 1, ensuring that all possible outcomes are accounted for.

Front

What is the expected number of successes in a Binomial distribution?

Back

The expected number of successes is given by E(X) = n * p.