Day1_Spring_2010_M360

# Day1_Spring_2010_M360 - Descriptive Statistics Exam 1...

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Descriptive Statistics: Exam 1 Variable N Mean StDev Min Q1 Med Q3 Max Exam 1 30 82.93 11.08 42.00 77 83 91.5 97

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Random Variables and Probability Distributions A coin is tossed four times and the number of heads is counted. How many outcomes are there in the sample space? Are the outcomes equally likely? What events are contained in the sample space? Are these events equally likely?
Random Variable – A random variable is a function that assigns a number to each outcome in the sample space. TTTT 0 HTTT 1 HHTT 2 HHHT 3 THHH 3 HTHT 2 Etc. x P(X=x) 0 1 2 3 4

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Random Variables – A random variable is a function that assigns a number to each outcome in the sample space. TTTT 0 HTTT 1 HHTT 2 HHHT 3 THHH 3 HTHT 2 Etc. x P ( X=x ) 0 1/16 1 4/16 2 6/16 3 4/16 4 1/16 4 ( ) 16 x C P x = Probability Distribution What is the sum of column 2?
Heads Percent 4 3 2 1 0 40 30 20 10 0 Probability Distribution P(X) : Probability of tossing  X  heads

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Heads Percent 4 3 2 1 0 40 30 20 10 0 Mean 2 StDev 1.033 N 16 Histogram of Heads Normal
Suppose that a fair coin is flipped 10 times and the number of heads is recorded. Construct the probability distribution Heads x P( X=x ) 0 ??? __ __ __ __ __ __ __ __ __ __ 1 ??? __ __ __ __ __ __ __ __ __ __ 2 ??? __ __ __ __ __ __ __ __ __ __ 3 4 P ( X = x ) = ??? 5 6 7 8 9 10

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Suppose that a fair coin is flipped 10 times and the number of heads is recorded. Construct the probability distribution Heads x P( X=x ) 0 0.000977 1 0.009766 2 0.043945 3 0.117188 4 0.205078 5 0.246094 6 0.205078 7 0.117188 8 0.043945 9 0.009766 10 0.000977 0 2 4 6 8 10 12 Number of Heads P(X = x) Sum = ??? 10 10 1 ( ) 2 x P X x C   = =    
Construct the probability distribution for the experiment where two dice are rolled and the sum of the faces is recorded. x 2 3 4 5 6 7 8 9 10 11 12 P ( X=x ) 1/36 2/36 3/36 4/36 5/36 6/36 5/36 4/36 3/36 2/36 1/36 6/36 5/36 4/36 3/36 2/36 1/36 2 3 4 5 6 7 8 9 10 11 12 What is the total area of the bars?

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Discrete Sample Spaces - If a sample space contains a finite number of outcomes, or a countably infinite collection of outcomes, it is called a discrete sample space and X is called a discrete random variable .
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## This note was uploaded on 05/14/2010 for the course MATH 360 taught by Professor Wallace during the Spring '10 term at SUNY Geneseo.

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Day1_Spring_2010_M360 - Descriptive Statistics Exam 1...

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