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Discrete Probability Distributions

What is the probability that the sum of two dice will be less than 5? How many throws will it take you to hit your first "bullseye" on a dart board? Use discrete probability distributions to find out!

Uniform Distribution

         

Jill has a set of \(33\) cards labelled with integers from 1 through \(33.\) She faces all the cards down, shuffles the deck repeatedly and then picks the card on the top. What is the probability that the card she picks shows a number larger than \(19?\)

Note: No two cards have the same number.

Which of the following represents the probability density function of a random variable \(X\) that takes on integers following the discrete uniform distribution \(X\sim U\{9,48\}?\)

Harry spins a roulette which consists of integers from 1 through \(14\) (not necessarily in order). What is the variance of the outcome he gets?

Note: The areas that correspond to each number are equal.

Find the sum of the expected value and variance of a random variable \(X\) which follows the discrete uniform distribution \(X \sim U\{5,18\}?\)

What is the expected value of the outcome when throwing a fair die?

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