6.2 Binomial distributions ( 2 )

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 is the formula for calculating the probability of exactly k successes in a binomial distribution?

Back

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

Front

What does 'at least k successes' mean in the context of binomial distributions?

Back

'At least k successes' means the probability of getting k or more successes in n trials.

Front

How do you calculate the probability of getting at least k successes?

Back

P(X >= k) = 1 - P(X < k) = 1 - P(X = 0) - P(X = 1) - ... - P(X = k-1).

Front

What is the difference between binompdf and binomcdf functions?

Back

binompdf calculates the probability of exactly k successes, while binomcdf calculates the cumulative probability of getting k or fewer successes.

Front

How do you find the probability of getting exactly 5 successes in 12 trials with a success probability of 0.3?

Back

Use the binompdf function: P(X = 5) = (12 choose 5) * (0.3)^5 * (0.7)^(12-5).

Front

What is the expected value (mean) of a binomial distribution?

Back

The expected value (mean) 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).

Front

How do you determine the number of outcomes with exactly k successes in n trials?

Back

Use the binomial coefficient: (n choose k) = n! / (k!(n-k)!).