Binomial Distribution: HUNTER

Front

What is a Binomial Distribution?

Back

A Binomial Distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent states and is defined by two parameters: the number of trials (n) and the probability of success (p).

Front

What are the parameters of a Binomial Distribution?

Back

The parameters of a Binomial Distribution are n (the number of trials) and p (the probability of success on each trial).

Front

What does X ~ B(n, p) represent?

Back

X ~ B(n, p) indicates that the random variable X follows a Binomial Distribution with n trials and a probability p of success.

Front

How do you calculate the probability of exactly k successes in a Binomial Distribution?

Back

The probability of exactly k successes in a Binomial Distribution is calculated using the formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k).

Front

What does P(X = k) mean in the context of Binomial Distribution?

Back

P(X = k) represents the probability of obtaining exactly k successes in n independent Bernoulli trials.

Front

What is the significance of the probability of success (p) in a Binomial Distribution?

Back

The probability of success (p) determines how likely it is to achieve a success in each trial, influencing the shape and spread of the distribution.

Front

What is the mean of a Binomial Distribution?

Back

The mean (expected value) of a Binomial Distribution is calculated as E(X) = n * p.

Front

What is the variance of a Binomial Distribution?

Back

The variance of a Binomial Distribution is calculated as Var(X) = n * p * (1 - p).

Front

What does P(X > k) represent?

Back

P(X > k) represents the probability of obtaining more than k successes in n trials.

Front

What does P(X ≤ k) represent?

Back

P(X ≤ k) represents the probability of obtaining k or fewer successes in n trials.