Chapter 4 Review

Front

What type of probability distribution is used for the number of events occurring in a fixed interval of time or space, such as house fire claims per month?

Back

Poisson distribution.

Front

If the average number of breakdowns of a conveyor belt in a month is 2.8, how do you find the probability of exactly two breakdowns occurring in that month?

Back

Use the Poisson probability formula: P(X=k) = (e^(-λ) * λ^k) / k!, where λ is the average rate (2.8) and k is the number of occurrences (2).

Front

What is a continuous random variable? Provide an example.

Back

A continuous random variable can take any value within a given range. Example: The time it takes a randomly selected student to complete an exam.

Front

What type of probability distribution should be used when determining the probability of a certain number of successes in a fixed number of trials, such as rolling a die multiple times?

Back

Binomial distribution.

Front

How do you calculate the mean of a probability distribution?

Back

The mean (expected value) is calculated as E(X) = Σ [x * P(x)], where x is the value and P(x) is the probability of x.

Front

What is the formula for the Poisson probability distribution?

Back

P(X=k) = (e^(-λ) * λ^k) / k!, where λ is the average number of occurrences and k is the number of occurrences.

Front

What is the significance of the parameter λ in the Poisson distribution?

Back

λ represents the average number of occurrences in a fixed interval.

Front

In a binomial distribution, what do the parameters n and p represent?

Back

n is the number of trials, and p is the probability of success on each trial.

Front

What is the variance of a Poisson distribution?

Back

The variance of a Poisson distribution is equal to λ.

Front

How do you determine the probability of obtaining a specific number of successes in a binomial distribution?

Back

Use the binomial probability formula: P(X=k) = (n choose k) * p^k * (1-p)^(n-k).