Geo,Bin,Poisson

Front

What is the probability of exactly k successes in n trials for a binomial distribution?

Back

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

Front

What is the mean of a binomial distribution?

Back

Mean (μ) = n * p, where n is the number of trials and p is the probability of success.

Front

What is the standard deviation of a binomial distribution?

Back

Standard Deviation (σ) = √(n * p * (1-p)).

Front

What is the expected value of a geometric distribution?

Back

Expected value (E) = 1/p, where p is the probability of success.

Front

What is the probability of the first success occurring on the k-th trial in a geometric distribution?

Back

P(X = k) = (1-p)^(k-1) * p.

Front

What is the formula for calculating combinations?

Back

n choose k = n! / (k! * (n-k)!), where n! is the factorial of n.

Front

What is the probability of getting exactly k heads when flipping a fair coin n times?

Back

P(X = k) = (n choose k) * (0.5)^k * (0.5)^(n-k).

Front

What is the Poisson distribution used for?

Back

The Poisson distribution models the number of events occurring in a fixed interval of time or space, given a known average rate of occurrence.

Front

What is the mean of a Poisson distribution?

Back

Mean (λ) = average number of events in the interval.

Front

What is the probability of observing k events in a Poisson distribution?

Back

P(X = k) = (λ^k * e^(-λ)) / k!, where e is Euler's number.