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s_m5_handouts

# s_m5_handouts - Rev F07 STA 2023 Module 5 Discrete Random...

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Rev. F07 http://faculty.valenciacc.edu/ashaw/ 1 STA 2023 Module 5 Discrete Random Variables Rev.F08 2 Learning Objectives Upon completing this module, you should be able to: 1. Determine the probability distribution of a discrete random variable. 2. Construct a probability histogram. 3. Describe events using random-variable notation, when appropriate. 4. Use the frequentist interpretation of probability to understand the meaning of probability distribution of a random variable. 5. Find and interpret the mean and standard deviation of a discrete random variable. http://faculty. valenciacc . edu/ashaw/ Click link to download other modules. Rev.F08 3 What is a Random Variable? What does it mean? A discrete random variable usually involves a count of something. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.

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Rev. F07 http://faculty.valenciacc.edu/ashaw/ 2 Rev.F08 4 What is a Probability Distribution? http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. This is an example of a probability distribution of a discrete random variable X , where x represents the possible number of siblings of a randomly selected student. Note the difference between X and x . Rev.F08 5 Probability Distribution and Probability Histogram The probability distribution and probability histogram of a discrete random variable show its possible values and their likelihood . http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Rev.F08 6 Probability Distribution and Probability Histogram (Cont.) http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Can you tell what is represented on the y -axis of the probability histogram?
Rev. F07 http://faculty.valenciacc.edu/ashaw/ 3 Rev.F08 7 Probability of an Event http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. The probability of the event that the students have exactly two siblings (when x is 2) can be represented by P( X = 2). In this case, P( X = 2) = 0.275. The probability of the event that the students have exactly three siblings (when x is 3) can be represented by P( X = 3). In this case, P( X = 3) = 0.075. Rev.F08 8 Probability of an Event (Cont.) http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. The probability of the event that the students have less than three siblings (when x is 3) can be represented by P( X < 3) . P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.200 + 0.425 + 0.275 = 0.900 The probability of the event that the students have less than two siblings (when x is 2) can be represented by P( X < 2) . P(X < 2) = P(X = 0) + P(X = 1) = 0.200 + 0.425 = 0.625 Rev.F08 9 Probability of an Event (Cont.) http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. The probability of the event that the students have less than or equal to two siblings (when x is 2) can be represented by P( X 2). P(X 2) = P(X = 0) + P(X = 1)+ P(X = 2) = 0.200 + 0.425 + 0.075 = 0.9 Note that P(X 2) = P(X < 3) = P(X = 0) + P(X = 1)+ P(X = 2) = 0.9.

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Rev. F07 http://faculty.valenciacc.edu/ashaw/ 4 Rev.F08 10 Probability of an Event (Cont.) http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
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s_m5_handouts - Rev F07 STA 2023 Module 5 Discrete Random...

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