Statistics 4.3 Practice

Front

What is a geometric distribution?

Back

A geometric distribution models the number of trials until the first success in a series of independent Bernoulli trials, where each trial has the same probability of success.

Front

What is the formula for the probability of success in a geometric distribution?

Back

The probability of success on the k-th trial is given by P(X = k) = (1-p)^(k-1) * p, where p is the probability of success.

Front

What is a Poisson distribution?

Back

A 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 formula for the probability of k events in a Poisson distribution?

Back

The probability of observing k events is given by P(X = k) = (e^(-λ) * λ^k) / k!, where λ is the average rate of occurrence.

Front

How do you calculate the mean of a Poisson distribution?

Back

The mean of a Poisson distribution is equal to λ, the average rate of occurrence.

Front

What is the relationship between the geometric distribution and the concept of 'failure' before the first success?

Back

In a geometric distribution, the number of failures before the first success is modeled, where each failure has a probability of (1-p).

Front

How do you find the probability of not making a sale in a series of calls using geometric distribution?

Back

To find the probability of not making a sale in the first n calls, use (1-p)^n, where p is the probability of making a sale.

Front

What is the significance of the mean in a Poisson distribution?

Back

The mean (λ) indicates the average number of occurrences in the given interval, and it is also the variance of the distribution.

Front

How do you interpret the result of P(4) when μ = 5 in a Poisson distribution?

Back

P(4) represents the probability of observing exactly 4 events when the average number of events is 5.

Front

What does it mean to find the probability of 'at most' a certain number of events in a Poisson distribution?

Back

Finding the probability of 'at most' k events means calculating the cumulative probability of observing 0, 1, 2, ..., k events.