? service tation has both self-serv1C2 and full-serv ce islands on each s and th

Question

? service tation has both self-serv1C2 and full-serv ce islands on each s and there is a sn e egular unleaded pump with two hoses Let tha ful-service island in usa at that tima. The jaint pmf of x and Y appaars in the a denota thu number o hoses being used on th self-serv ce island at a particuar rme and et Y denote e number o hoses on (a) what is p(X-1 and Y-1)? (b) Compute Ax 1 and Y1) (c) Grven hases ara baing used an tha salf-sarvica iland, what i the prabablity at least I hnsa is haing used at tha hul-sarvica islana (ua 5 signtcant digits)- Compute uhve probablity or uis event, ?(X O and ? # O)-L (d) Compute the marginal pmt ot x Compute the Expected number or hoses benng used on the set service sland. Computc the marginal pmf of Y. compute the Expactad number of bases bang used on the ful-servic??? Gland. Siven EtxYJ is 1.s0uo, cumpute the Covariancex,Y1 (hint: use shorteut formule; Use S sigrificant digits). rr var..s o. 5331 and Varty'Jis 0.5876, then compute the Correatorp?VJ (Use 5 signt,cant digits? () Are X and independent *? Fxplain. X and Y dre independent because Arx,y)? PM)·Pr(y x and ? are independent because /(x,y)-Rx(x) . Pr(v). 0 x and ? are not independent because ?(x,y)-Px(x)-pry). , PM. x and ? are not independant because ?(x,y)-PN(x)

Explanation / Answer

a) P(x=1 and y=1) = the intersection of both x and y as 1 which is easily visible from the table = 0.2 (the intersection of the row and column's 1 value)

b) P(X<=1 and Y<=1) = fist 2X 2 matrix's sum = 0.1+0.04+0.06+0.2 = 0.4 (where each X and Y has a value of <=1)

c) P(X=/= 0 and Y =/= 0) = 1- P(X=0 and Y=0) = 1-0.1 = 0.9

d)  P(X|x=0) = 0.1+0.04+0.01 = 0.15

P(X|x=1)= 0.06+0.20+0.07 = 0.33

P(X|x=2) = 0.06+0.14+0.32 = 0.52

So., x 0 1 2

P(x) 0.15 0.33 0.52   

As per the Chegg policy we are supposed to answer 1st question only with all its 4 subparts. So here I have provided the solution of the 1st question's 4 sub parts. If you want the answer for the rest kindly post them seperately.

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