Geometric vs. Binomial

Front

What is a continuous random variable?

Back

A continuous random variable can take any value within a given range. For example, the time it takes for a student to complete an exam.

Front

What is a binomial variable?

Back

A binomial variable counts the number of successes in a fixed number of independent trials, each with the same probability of success.

Front

What is a geometric variable?

Back

A geometric variable counts the number of trials until the first success occurs.

Front

What is the probability of winning a game piece if the chance is 1 out of 4?

Back

The probability of winning is 0.25 or 25%.

Front

In a binomial distribution, what are the two possible outcomes?

Back

Success and failure.

Front

What does it mean if a distribution is skewed right?

Back

A right-skewed distribution has a longer tail on the right side, indicating that there are a few high values.

Front

How do you calculate the probability of at least k successes in a binomial distribution?

Back

Use the cumulative distribution function (CDF) or calculate 1 minus the probability of fewer than k successes.

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 is 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 variance of a binomial distribution?

Back

Var(X) = n * p * (1-p), where n is the number of trials and p is the probability of success.