Prob and Stat - FINALS PRACTICE #5

Front

What is the expected value in a probability game?

Back

The expected value is the average outcome of a probability game, calculated by multiplying each possible outcome by its probability and summing these products.

Front

How do you determine if a game is fair?

Back

A game is considered fair if the expected value is zero, meaning that on average, players neither win nor lose money.

Front

What is a Poisson distribution?

Back

A Poisson distribution models the number of times an event occurs in a fixed interval of time or space, given a known average rate of occurrence.

Front

What is the formula for calculating the probability of exactly k events in a Poisson distribution?

Back

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

Front

What is the mean in a probability distribution?

Back

The mean is the average value of a random variable, representing the center of the distribution.

Front

What is a binomial experiment?

Back

A binomial experiment consists of a fixed number of independent trials, each with two possible outcomes (success or failure), and the probability of success is constant.

Front

What are independent trials in probability?

Back

Independent trials are experiments where the outcome of one trial does not affect the outcome of another.

Front

What is the significance of the number of trials in a binomial experiment?

Back

The number of trials determines how many times the experiment is conducted, affecting the distribution of outcomes.

Front

What is the probability of getting exactly k successes in n trials of a binomial experiment?

Back

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

Front

What is the difference between discrete and continuous probability distributions?

Back

Discrete distributions deal with countable outcomes, while continuous distributions deal with outcomes that can take any value within a range.