test2_f05sol

test2_f05sol - from 6 E(X)=3.17...

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Solutions to ST 370 Online Second Exam, Fall 2005 1. .22 = Pr(BC is beaten)* Pr(MTS is beaten)*Pr(M is beaten)= .4*.9*.6=.216 2. 6/9 (9 possible values: (1,1)->X=1, (1,2)->X=2, etc.: 1,2,3,2,4,6,3,6,9 each with prob. 1/9) 3. .874 = Pr(-1.23 < Z < 2.13)= Pr(Z < 2.13) - Pr(Z < -1.23) 4. .94 (here lambda*t=6; we need to find Pr(X>=3)=1-Pr(X<=2)= 1- [Pr(X=0)+ Pr(X=1)+Pr(X=2)]= 1- exp^(-6)[1+6+36/2]=1-exp^(-6)*25= 1-.06196. Or from Table C, 1-Pr(X<=2)=1-.0620=.09.) 5. .227 =Pr( X>83)=Pr(Z > (83-80)/4) = Pr(Z > .75) = 1 - Pr(Z <= .75) =1 - .7734 = .2266; where Z is the standard normal distribution 6. 76.6 = (-.84)*4+80=76.6 7. 3.17 =E(X)=4*.5+3*.3+2*.1+1*.07 =3.17 8. 1.06 (first calculate E(X^2)= 16*.5+9*.3+4*.1+1*.07=11.17,
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Unformatted text preview: from 6. E(X)=3.17; sd(X)=sqrt(11.17-3.17^2)=1.06) 9. Binomial (# of "successes" in n independent trials with success="die stays on the plate") 10. A list of all possible outcomes 11. .86 = int(0,2/lambda) lambda*exp(-lambda*t)dt = [-exp(-lambda*t)](0,2/lambda)=1-e^(-2)) 12. 2.333 =int(1,4)[x/{2*sqrt(x)}]dx=int(1,4)[sqrt(x)/2]dx=x^{3/2}/3[1,4] =4^{3/2)/3-1/3=7/3 13. .268 =int(3,4)[1/{2*sqrt(x)}]dx=sqrt(x)[3,4]=sqrt(4)-sqrt(3)=2-1.732=.2679 14. B. 15. .582 16. .984 from Table A 17. Always since Pr(A and B) = Pr(A) + Pr(B) - Pr(A or B) can be rearranged to Pr(A or B) = Pr(A) + Pr(B) - Pr(A and B) a basic formula 18. .16(=16/100) 19. .25(=2/8) 20. None of the above (=16/24)...
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This note was uploaded on 01/16/2012 for the course ST 370 taught by Professor Nail during the Spring '08 term at N.C. State.

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