Let X1,X2, . . . ,X18 be a random sample of size 18 from a chi-square distribution with r = 1. Recall that

μ = 1 and σ2 = 2.

(a) How is distributed?

(b) Using the result of part (a), we see from Table IV in Appendix B that P(Y ≤ 9.390) = 0.05 and P(Y ≤ 34.80) = 0.99.Compare these two probabilities with the approximations found with the use of the central limit theorem.

Reference Table IV in Appendix B

GenBus306Session9: RandomVariables Forcaseupdates Assume15%telephonebookings Nowthatweknowaboutprobability,howdowemakedecisionsinvolvingrisk Tomakeadecision,weneedtoknowpossibleoutcomes(radonvariables)and probabilitiesofoutcomes(distributions) Arandomvariable(canbecontinuousordiscrete)associatesanumericvaluewitheach possiblerandomoutcome Forexample: • Lotteryoutcomes • #ofstudentsinclasstoday • futurestockprices • #ofcustomersthatwalkintoastore Anygambleisarandomvariable Randomvariablescanhavedifferentdistributions:thenormalbellcurveisthemost common Inclasswealsocoveruniformandanotherthatstartswithab Theexpectedvalueofadiscreterandomvariableistheprob