T111soln - STAT 330 TEST 1 SOLUTIONS 1. Suppose X NB2, p...

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STAT 330 TEST 1 SOLUTIONS1. SupposeXNB2,pwith p.f.fx2xp2qx,x0,1,....;q1p; 0p1.a 3ShowEXkEXX1  Xk12kqpk,k1,2,....EXkxkxk2xp2qxp22kxk2kxkqxsincexk2x2k2kxkp22ky02kyqykby lettingyxkp22kqky02kyqyp22kqk1q2kby the Binomial Seriesp22kqkp2ksince 1qp2kqpk.b 2Useato findVarX.VarXEX2EXEX222qp22qp2qp26q2p22qpp24q2p21p26q22q1q4q2sincep1q2qp2c 3FindMtEetX, the m.g.f. ofX. For what values oftdoesMtexist?Mtx0etx2xp2qxp

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Term
Spring
Professor
PAULASMITH
Tags
Statistics, Taylor Series, Normal Distribution, Probability distribution, probability density function, Scale parameter

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