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# Pg 67 - 29 The Central Limit Theorem 0 Let X1.Xn be...

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Unformatted text preview: 29 The Central Limit Theorem 0 Let X1, . . .Xn be independent random variables each with the same distribution and E [X] : u and Var/1X] : 02 < 00. Let S.” and .7551 the sum and sverege respectively; 5,, : X1+...+Xn is i=1 1 1 11:1 71 II a The central limit thaorem says that sums and averages have an approximate normal distribution when n is sufﬁciently large. ‘ 5n m 1V(np1n02) '1“ a: ‘7, _ W m s3 , ; ‘2 a. 3'” _ .P‘T‘” M .2 X ~N ([1,, n) Em ”1- i; if? ‘1”ng M ,% o For simulation to give you the intuitive. behind this, go to the following simulation Wimxufiiceedu [mlane / st at sin} / s umplingﬂist / 0 Example: Let X1, . . . ,Xn be output voltages of pressure sensors which have an ex— ponential distribution with u mean of 5. Suppose there are 49 such pressure sensors. V’tht is the approximate distribution, mean, and variance of the average voltage? {Sousa Mg mix} it ‘4“ 25 ; n27? a sews—5%} o Read Sections 6.10 0 Problems in Section 6.10: 6.31 67 cm;- H: n if: fewer“ two“ a“: v 3" 1“ ’3'} W/ ...
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