ZTZ Prob and Stat Dec 16

Front

What is a Poisson distribution?

Back

A Poisson distribution is a probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space, given that these events occur with a known constant mean rate and independently of the time since the last event.

Front

What is the formula for the probability of getting k occurrences in a Poisson distribution?

Back

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

Front

What does it mean if a distribution 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 characterized by a fixed number of trials, a constant probability of success, and independent trials.

Front

What are the assumptions of a Binomial distribution?

Back

1. The number of trials is fixed. 2. Each trial has only two possible outcomes (success or failure). 3. The probability of success is constant across trials. 4. Trials are independent.

Front

What is the probability of getting 0 occurrences in a Poisson distribution with a mean of 4?

Back

P(X=0) = e^(-4) which is approximately 0.0183.

Front

What is the difference between independent and dependent trials in probability?

Back

Independent trials are those where the outcome of one trial does not affect the outcome of another, while dependent trials are those where the outcome of one trial influences the outcome of another.

Front

What is an example of a situation that is NOT a Binomial distribution?

Back

Asking teachers if they have kids is not a Binomial distribution because the probability of success (having kids) is not constant and the trials are not independent.

Front

What is an example of a situation that is a Binomial distribution?

Back

Checking 7 cars in a parking lot for parking passes is a Binomial distribution because there are a fixed number of trials (7), each trial has two outcomes (pass or no pass), and the trials are independent.

Front

What is a probability distribution?

Back

A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can take.

Front

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

Back

The mean (λ) in a Poisson distribution indicates the average number of occurrences in a given interval.