Basic Binomial Distribution

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 outcomes under a given number of trials.

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 an individual trial).

Front

What does P(X=k) represent in a Binomial Distribution?

Back

P(X=k) represents the probability of getting exactly 'k' successes in 'n' trials.

Front

What is the formula for calculating Binomial Probability?

Back

The formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where (n choose k) = n! / (k!(n-k)!).

Front

What does the term 'success' mean in the context of Binomial Distribution?

Back

In Binomial Distribution, 'success' refers to the outcome of interest, which can vary depending on the context of the problem.

Front

What is the difference between P(X≤k) and P(X

Back

P(X≤k) includes the probability of getting 'k' successes, while P(X

Front

How do you interpret P(X>k)?

Back

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

Front

What is the significance of the cumulative distribution function (CDF) in Binomial Distribution?

Back

The CDF gives the probability that a random variable is less than or equal to a certain value, allowing for the calculation of probabilities for ranges of outcomes.

Front

What is the expected value (mean) of a Binomial Distribution?

Back

The expected value is calculated as E(X) = n * p.

Front

What is the variance of a Binomial Distribution?

Back

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