Chapter 5

# Chapter 5 - Chapter 5 Discrete Probability Distributions...

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Chapter 5 Discrete Probability Distributions

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Let’s start with Random Variables A random variable is simply a variable ( x ) whose value depends on the outcome of a chance operation Let’s say you want to roll 2 dice and find the sum total spots showing on top. The random variable = sum total spots showing The possible outcomes are number 2 through 12
Another example You toss 4 coins and are interested in the number of heads showing Random Variable: number of heads showing Possible outcomes: 16 possible outcomes

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So for a random variable : Outcome based on chance operation 1 outcome per run of the chance operation Every outcome is independent of every other outcome Does flipping 4 coins (all at same time) meet these requirements?
Numerical Random Variables can be divided into 2 groups Discrete Random Variables (Chapter 5) quantitative discrete Continuous Random Variables (Chapter 6) quantitative continuous

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Discrete vs. Continuous You randomly sample groups of 5 fruitflies and count the number that are black vs. the number that are grey You randomly sample children and measure their blood lead levels to look for lead poisoning You randomly sample middle-aged men and measure their systolic blood pressure
Ch. 5: Discrete Random Variables Let’s consider rolling a single die There are 6 sides, progressing from 1 dot to 6 dots If it’s a fair die, then each side equally likely Can use a Probability Function : P ( x ) = 1/6 for x = 1, 2, 3, 4, 5, 6 Or a Probability Distribution to describe relationship x 1 2 3 4 5 6 P ( x ) 1 6 1 6 1 6 1 6 1 6 1 6 Sum of all probabilities must sum to 1

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Probability Histogram Can show this graphically – Probability Histogram Probabilities for a 6-sided die 0 0.05 0.1 0.15 0.2 1 2 3 4 5 6 value on die Probability of that value -All possible outcomes listed, -Each outcome mutually exclusive -Sum of all probabilities = 1
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) What about rolling 2 dice Here are the possible outcomes (1 st die, 2 nd die) Sum the number of dots showing on the 2 dice. What is the probability distribution for the sum total ?

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Probability Histogram for rolling 2 dice 0 5 10 15 20 1 2 3 4 5 6 7 8 9 10 11 12 Total dots showing Probability (%) Again show all possible , mutually exclusive outcomes. THIS IS ALL POSSIBLE OUTCOMES THAT COULD OCCUR when you roll 2 dice. NOW: How likely 1 event is compared to another?
Another Example : Family Size A large sample of Seattle households were selected at random and the following data were collected: P (0 Children) = 0.25 P (1 Child) = 0.35 P (2 Children) = 0.30 P (3 Children) = 0.09 P (4 Children) = 0.01 Assume very, very few people have >4 children Type of Variable?

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## This document was uploaded on 11/04/2011 for the course BIOM 301 at Maryland.

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Chapter 5 - Chapter 5 Discrete Probability Distributions...

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