Lecture17Sept08

# Lecture17Sept08 - Random Variables Sept. 19 Sample Spaces...

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Random Variables Sept. 19

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Sample Spaces and Outcomes Roll 2 dice and report the sum. Should we consider the sample space to be the possible rolls or the possible sums? Toss 5 coins and report the number of heads. Should we consider the sample space to be the sequences of heads and tails or the numbers 0 through 5?
Random Variables A random variable is a function from a sample space to the real numbers. To avoid the case where we just use the numbers as labels, we consider the function to be a random variable only if taking the average makes sense.

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Sample Spaces and Outcomes Roll 2 dice and report the sum. We can consider the sample space to be the possible rolls and observe the random variable f(a,b)=a+b Toss 5 coins and report the number of heads. We can consider the sample space to be the sequences of heads and tails and observe the random variable f(a,b,c,d,e)=#Heads
Discrete Random Variables A random variable is said to be discrete if it takes on a finite or countable set of values. A binary outcome such as head/tail, true/false or

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## This note was uploaded on 09/16/2008 for the course STAT 414 taught by Professor Senturk,damla during the Fall '07 term at Penn State.

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Lecture17Sept08 - Random Variables Sept. 19 Sample Spaces...

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