Probability Distributions and Payoff Values

Front

What is a probability distribution?

Back

A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

Front

Define expected value in probability.

Back

The expected value is the long-term average or mean of a random variable, calculated as the sum of all possible values, each multiplied by its probability.

Front

How do you calculate the expected value of a discrete random variable?

Back

Multiply each possible value of the random variable by its probability and sum all the results.

Front

What is the formula for expected value (E(X))?

Back

E(X) = Σ [x * P(x)], where x is a value and P(x) is the probability of x.

Front

What does it mean if the expected value is positive?

Back

A positive expected value indicates that, on average, a player can expect to gain money from the game.

Front

What does it mean if the expected value is negative?

Back

A negative expected value indicates that, on average, a player can expect to lose money from the game.

Front

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

Back

The mean represents the central tendency of the distribution, indicating where most values are concentrated.

Front

How do you find the probability of multiple outcomes in a probability distribution?

Back

Add the probabilities of the individual outcomes together.

Front

What is a random variable?

Back

A random variable is a variable whose possible values are numerical outcomes of a random phenomenon.

Front

What is the difference between discrete and continuous random variables?

Back

Discrete random variables have countable outcomes, while continuous random variables can take any value within a given range.