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Unformatted text preview: ers and 99% true negative results for non drug users. Suppose that 0.5% of people are users of the drug. If a randomly selected individual tests positive, what is the probability he or she is a user? FINDING THE INVERSE CONDITIONAL PROBABILITY [THIS WILL BE A HW 2 PROBLEM] Random variables: Chapter 9
v༇ Random Variable is a variable whose value depends
on the outcome of a random phenomenon.
Abstract definition:
A random variable is a function defined on S.
Recall, S = sample space = {all possible outcomes}
This function assigns a value to each
possible outcome. The value is typically a
number. Example of a random variable
Toss a coin 3 times. Let X = number of “heads”.
Outcome TTT TTH THT HTT HHT HTH THH HHH Value of X 0 1 1 1 2 2 2 3 Each elementary outcome in S has probability 1/8 What is P(X=1)? Write distribution table for X? Random Variables
v༇ Discrete random variable: Possible values can be
counted or listed
q༇ e.g. the number of defective units in a batch of 20 v༇ Continuous random variable: May assume any
numerical value in one or more intervals
q༇ e.g. height of students. Discrete Random Variable
v༇ Probability distribution of a discrete random variable
is a table, graph or formula that gives the probability
associated with each possible value that the variable
can assume.
v༇ e.g. X = number of heads in 3 tosses
Value 0 1 2 3 Probability 1/8 3/8 3/8 1/8 Discrete Random Variable & Expected
Values: A COIN TOSS GAME
v༇ Game:
q༇ Toss a coin 3 times. I will pay you 1$ for each head. v༇ If you play this game 1000 times, how much money
do you expect to win on an average?
Distribution TABLE Value
Probability 0
1/8 1
3/8 2
3/8 3
1/8 v༇ Answer:
q༇ Weighted Mean: contribution of the values is
proportional to their probabilities. Discrete Random Variables:
Distribution Table
v༇ We denote the value...
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This note was uploaded on 01/15/2014 for the course BUAD 310 taught by Professor Lv during the Fall '07 term at USC.
 Fall '07
 Lv

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