Commication

DMD Assignment 1. (3.7) (a) firstly, suppose it is Normally distribution, we know the mean of the retire apples weight is 4.2(µ=4.2), the banal deviation is 1.0(?=1.0). suck up that the weight of tomato is dependent. The tomatoes ar sold in big bucks of three. ?~N(nµ, ?n?). E(?)=3*µ=12.6 ?(?)= ?3*?=1.7321 (b) P(11.0???13.0)=P{(11-12.6)/1.7321?(?-E(?))/?(?) ?(13.0-12.6)/1.7321} =0.5910-0.1788=0.4122=41.2% 2. (3.9) Let X denote the region increase in the Dow Jones Index. Let Y denote the parting increase in S& amp;P five hundred index. view X and Y obey a conjugation Normal distribution. The mean of X is 11% (µx=0.11), the bill deviation of X is 13% (?x=0.13). the mean of Y is 10%(µy=0.10), the standard deviation of Y is 12% (?y=0.12). Suppose CORR(X,Y)=0.43. (a)P(X?0.11)=1-P{(X-µx)/ ??(0.11-0.11)/0.13} =1-F (0) =1/2=50% (b)P(X?-0.11)=P{(X-µx)/?x?(-0.11-0.11)/0.13} =F(-1.69)=0.0455=45.5% (c)P(0?Y?0.15)=P{(X-µy)/?y?(0. 15-0.10)/0.12}-P{(X-µy)/?y?(0-0.10)/0.12} =0.6628-0.20=46.3% (d) Suppose A is the portfolio of Dow Jones index and S&P index. So, E(A)=0.3*0.11+0.7*0.10=0.103 Var(A)=0.32*0.132+0.72*0.122+2*0.3*0.7*0.43*0.13*0.12=0.01138 ?(A)=0.1067 (e) (X-Y) overly obeys Normal distribution. µ(x-y) =0.01, ?(x-y) =0.13. (X-Y)~N (0.01, 0.

13) P{ (X-Y) ?0}=1-P{ (X-Y)- µ(x-y)/ ?(x-y)?(0-0.01)/0.13}=1-F(-0.0415)=0.532=53.2% 3. (3.15) (a) We quite a little turn over from the content of the problem, assume and infer that the quantity of X ~ binomial (n, p). So, assume S=X1+X2++Xn, n=2500, p=0.1. E(S) = n*p=250, ?s= 15 (b) Revenue: assume Y be the returned re! venue item. Y~ Binomial (n, p). E( Y) =500*250-Sn*500=125,000-500*Sn =1125000; ?y=335.4 (c ) assume the Z be the item, P(Z?1,300,000) =1-P(Z?1,300,000-1125000/335.4) =1-P(521.77)=0 4.(3.18) (a) The assumptions are that the probability of hazardous problem happened is in depended from each other, and also obey the identically distribution. The assumptions appear to be...If you want to get a full essay, put up it on our website: OrderCustomPaper.com

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