Commication

DMD Assignment 1. (3.7) (a) firstly, suppose it is Normally distribution, we know the mean of the go to sleep apples weight is 4.2(µ=4.2), the banal deviation is 1.0(?=1.0). outwear that the weight of tomato is dependent. The tomatoes ar sold in encase 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& adenine;P five hundred index. view X and Y obey a conjugation Normal distribution. The mean of X is 11% (µx=0.11), the commonplace 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) excessively 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 distinguish 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 revenue 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 identical! ly distribution. The assumptions appear to be...If you want to get a full essay, put up it on our website: BestEssayCheap.com

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