The main property of a discrete joint probability distribution can be stated as the sum of all non-zero probabilities is 1. The next line shows this as a formula. The marginal distribution of X can be ...

Amusement park patrons, wanting to go on a log ride, might not have to wait in line at all, they might have to wait for hours, or the wait could be anywhere in between. For a random log rider, the ...

The joint probability density function \(f\) of two random variables \(X\) and \(Y\) satisfies, for every \(a_1 b_1\) and \(a_2 b_2\), \[ P(a_1\le X\le b_1, a_2\le Y ...

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The Virginia Lottery offers a game called the New Year's Millionaire Raffle for which the top prize is one million dollars. There are 375,000 tickets sold, of which 508 are winners. There are three ...

Continuous Variable: can take on any value between two specified values. Obtained by measuring. Discrete Variable: not continuous variable (cannot take on any value between two specified values).

A discrete random variable is a type of random variable that can take on a countable set of distinct values. Common examples include the number of children in a family, the outcome of rolling a die, ...

The total area under the curve must equal 1, representing the fact that the probability of some outcome occurring within the entire range is certain. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...