Question

Let X denote the number of times a photocopy machine will malfunction: 0,1,2, or 3 times, on any given month. Let Y denote the number of times a technician is called onan emergency call. The joint p.m.f. p(x,y) is presented in the table below: y\. 0 1 2 3 0 0.15 0.30 0.05 0 1 0.05 0.15 0.05 0.05 2 0 0.05 0.10 0.05 Px(2) 0.20 0.50 0.20 0.10 py(y) 0.50 0.30 0.20 1.00 (a) Find the probability distribution of W = X+Y. (b) Find the probability distribution of V=X.Y.

Answer 1

function which evaluates the We prepare a table the values of Y. We Yearrange r v X and are P.m. f and write its Let W X +Y V= X- Y The column to pairs (X, Y) write in a we evaluate W V X POX,Y) W xtY V = X-Y о o. 15 O O.05 1 с 2 2. 1 C O.30 O.15 1 2. 2 O.O5 3 2. O.05 о O.05 2 2 O.10 4- 4 3 O O.05 4 O.o 5 2 5 6 OO NO N C O-

of W X+Y distribution o) Find Probabili ty W x+Y PCW) =O. 15 O 0.05+ 0.30 0-35 2 0+0.150.05 = 0.20 3 0.05+0.050 = o-\0 o.10o.05 =0.15 O.05 5 = 1 b Find the Probability distribution of V = X-Y PCV) O-15+0.05 +0+ o.30to.05 0 = O.55 = O.15 O.15 O.O5 O.05 2 0.10 = o.05 O o5 O 10 = O.10 4 O.05 ΣΡ() = 1

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