Umm Al-Qura University بسم الله الرحمن الرحيم Umm Al-Qura University Health Sciences College at Al-Leith Department of Public Health Lecture (5)

Random variables

Objectives: 1/ Define basics of Random variables. 2/ Define Types of Random variables 3/ Give an Example of Random variables .

Random variables A Random Variable is a set of possible values from a random experiment. Tossing a coin: we could get Heads or Tails. Let's give them the values Heads=0 and Tails=1 and we have a Random Variable "X": X = {0, 1} statistic

Random Variable X = "The score shown on the top face". Throw a die once Random Variable X = "The score shown on the top face". X could be 1, 2, 3, 4, 5 or 6 So the Sample Space is {1, 2, 3, 4, 5, 6} statistic

Types of Random Variables Discrete: Takes integer values Binary: Will an individual default (X=1) or not (X=0)? How many messages arrive at a switch (customers at a service point) per unit of time? Finite: How many female children in families with 4 children; values = 0,1,2,3,4? Infinite: How many people will catch a certain disease per year in a given population? Values = 0,1,2,3,… (How can the number be infinite? It is a model.) Continuous: A measurement. How long will a light bulb last? Values X = 0 to ∞ Performance of financial assets over time How do we describe the distribution of biological measurements? Measures of intellectual performance statistic

Cumulative Distribution Function (cdf): Continuous Cumulative Distribution Function (cdf): statistic

F(x)=P(X≤x)=∑f(x) Probability distribution function (pdf) : Discrete Probability Density Function (pdf) : F(x)=P(X≤x)=∑f(x) statistic

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P(X = value) = probability of that value Throw a die once X = {1, 2, 3, 4, 5, 6} In this case they are all equally likely, so the probability of any one is 1/6 P(X = 1) = 1/6 P(X = 2) = 1/6 P(X = 3) = 1/6 P(X = 4) = 1/6 P(X = 5) = 1/6 P(X = 6) = 1/6 statistic

The three coins can land in eight possible ways: statistic

Two dice are tossed The Random Variable is X = "The sum of the scores on the two dice". Let's make a table of all possible values statistic

statistic

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Exercise 9 Two coins are tossed. If Y represents the number of tails, what is P(Y = 1)? statistic

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