WorkSheet 5

Let S be the sample space for (X Y ) and for every element ? of S we have

E ( X Y ?S X ?Pr ?S X ?Pr EX EY

E [ (X - EX )2] E [ (X - EX (X - EX )] Using algebraic expansion , we get E [ X2 - 2X ?EX (EX )2] E X2 - 2E (X ?EX E (EX )2 Using the rule that the expectation value of

the sum is the sum of the expectation values EX2 - 2EX ?EX ( EX )2 The expectation of EX is EX and the expectation

of

(EX )2 is (EX )2 EX2 - 2 (EX )2 (EX )2 Simplifying the previous equation we get EX2 - (EX )2

s ( 1 2 2 3 4 7 9 /7 28 /7 4

The standard deviation ?s is computed using the formula given below 2 .94392

c ) What is the median of the sample s ? Explain how you came to this conclusion d ) Can you give a sample of 5 numbers in which the mean is more than twice the median (Write down all three , the sample of numbers , its median and its mean e ) Explain why some people argue the median is a better indicator for a typical value ' in a sample than the mean

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an will be a better indicator for a typical value if the mean is used instead...