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Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

Given descriptions of  3 random variables, decide whether or not each is from a Poisson or Binomial distribution.

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

$X \sim \operatorname{Binomial}(n,p)$. Find $P(X=a)$, $P(X \leq b)$, $E[X],\;\operatorname{Var}(X)$.

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Three parts. A sample of size $n$ is taken from $N$ where $k$ of the items are known to be defective and the task is to find the probability that more than $m$ defectives are in the sample. First part is sampling with replacement (binomial), second is sampling without replacement, (hypergeometric) and the last part uses the Poisson approximation to the first part.

$X \sim \operatorname{Binomial}(n,p)$. Find $P(X=a)$, $P(X \leq b)$, $E[X],\;\operatorname{Var}(X)$.

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.