G the number of defective units in a batch of 20 v

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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.

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