HW Solution 3

HW Solution 3 - STAT430 Summer 2009 Hui Nie STAT 430...

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STAT430 Summer 2009 Hui Nie STAT 430 Solution 3 Page 224 5.15 Solution (a) ( 5) (0.83) 0.7967 PX >= Φ = (b) (4 16) 2 (1) 1 0.6826 << = Φ− = (c) ( 8) 1 (0.33) 1 0.6293 0.3707 <=− Φ =− = (d) ( 20) (1.67) 0.9525 <= Φ = (e) ( 16) 1 (1) 0.1587 Φ = 5.17 Solution Let X be the number of points scored. Then, ( ) 10*1/10 5*2 /10 3*2 /10 2.6 EX =+ + = 5.26 Solution Let X be the number of heads that we get, then, ( | ) ( 524.5 | 0.5) 1 (1.55) 0.0606 PFa l se Fa i r p =≥ = = Φ = and ( | ) ( 524.5 | 0.55) 1 (1.62) 0.0526 P False Biased P X p = = Φ = 5.28 Solution Let X be the number of lefthanders. Assuming that X is approximately distributed as a binomial random variable with parameter n=200, p=0.12. Since (1 ) 21.12 10 np p => , we can use normal distribution to approximate this binomial random variable X. Then, with Z being a standard normal random variable, ( 19.5) ( 0.98) 0.8365 PZ > −= 5.32 Solution Let X be the time required to repair a machine, then, (a) 1 ( 2) exp( 2*1/ 2) e = 1
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STAT430 Summer 2009 Hui Nie (b) 0.5 exp( 10*1/ 2) (1 0 | 9 ) exp( 9*1/ 2) PX X e ≥> = = Page 227 5.7 Solution 22 () | | SD aX b Var aX b a a σ += = 5.9 Solution
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This note was uploaded on 06/28/2009 for the course STAT 430 taught by Professor Krieger during the Summer '08 term at UPenn.

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HW Solution 3 - STAT430 Summer 2009 Hui Nie STAT 430...

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