Discrete Distributions Random Variable A numerical variable whose

Discrete Distributions

Random Variable • A numerical variable whose value depends on the outcome of a chance experiment

Two types: • Discrete – count of some random variable • Continuous – measure of some random variable

Discrete Probability Distribution • Gives the values associated with each possible x value • Usually displayed in a table, but can be displayed with a histogram or formula

Properties for a discrete probability distribution 1) For every possible x value, 0 < P(x) < 1. 2) For all values of x, Σ P(x) = 1.

Suppose you toss 3 coins & record the number of heads. The random variable X defined as. . . The number of heads tossed Create a probability distribution. X P(X) 0. 125 1. 375 2. 375 3. 125 Create a probability histogram.

Let x be the number of courses for which a randomly selected student at a certain university is registered. X 1 2 3 P(X). 02. 03. 09 4 5 6 7 ? . 40. 16. 05 Why does this not start at zero? . 25 P(x = 4) = P(x < 4) =. 14 P(x < 4) =. 39 P(x > 5) =. 61 What is the probability that the student is registered for at least five courses?

Formulas for mean & variance Found on formula card!

Let x be the number of courses for which a randomly selected student at a certain university is registered. X 1 2 3 4 5 6 7 P(X). 02. 03. 09. 25. 40. 16. 05 What is the mean and standard deviations of this distribution? μ = 4. 66 & σ = 1. 2018

Here’s a game: If a player rolls two dice and gets a. Asum of 2 is or 12, fair game one where the cost to play EQUALS he wins $20. the. If he gets a expected value! 0 $5. 5 The cost 20 7, X he wins to P(X) 7/9 1/6 1/18 roll the dice one time is $3. Is this game fair? NO, since m = $1. 944 which is less than it cost to play ($3).

Linear function of a random variable The mean is changed If xbyis addition a random&variable and a and b aremultiplication! numerical constants, then the random variable y is defined by • and The standard deviation is ONLY changed by multiplication!

Let x be the number of gallons required to fill a propane tank. Suppose that the mean and standard deviation are 318 gal. and 42 gal. , respectively. The company is considering the pricing model of a service charge of $50 plus $1. 80 per gallon. Let y be the random variable of the amount billed. What is the mean and standard deviation for the amount billed? μ = $622. 40 & σ = $75. 60

Just. Linear add or subtract combinations the means! If independent, always add the variances!

A nationwide standardized exam consists of a multiple choice section and a free response section. For each section, the mean and standard deviation are reported to be mean SD MC 38 6 FR 30 7 If the test score is computed by adding the multiple choice and free response, then what is the mean and standard deviation of the test? μ = 68 & σ = 9. 2195