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Margaret considers five purchases in the amounts 5, 17, 21, 8, 15 dollars with respective probabilities 0.37, 0.22, 0.38, 0.81, 0.63. Anne contemplates sixpurchases in the amounts 8, 15, 12, 18, 15, 12 dollars. with respective probabilities 0.77, 0.52, 0.23, 0.41, 0.83, 0.58. Assume that all eleven possible purchases form anindependent class.
cx = [5 17 21 8 15 0];pmx = minprob(0.01*[37 22 38 81 63]);cy = [8 15 12 18 15 12 0];pmy = minprob(0.01*[77 52 23 41 83 58]);[X,PX] = canonicf(cx,pmx);[Y,PY] = canonicf(cy,pmy);icalc
Enter row matrix of X-values XEnter row matrix of Y-values Y
Enter X probabilities PXEnter Y probabilities PY
Use array operations on matrices X, Y, PX, PY, t, u, and PM1 = u>= 2*t;
PM1 = total(M1.*P)PM1 = 0.3448
M2 = u - t>=30;
PM2 = total(M2.*P)PM2 = 0.2431 James is trying to decide which of two sales opportunities to take.
Let X be the net profit on the first alternative and Y be the net gain on the second. Assume the pair is independent.
cx = [310 380 350 0];pmx = minprob(0.01*[35 41 57]);Y = 100*[0:8];PY = ibinom(8,0.57,0:8);
canonicEnter row vector of coefficients cx
Enter row vector of minterm probabilities pmxUse row matrices X and PX for calculations
Call for XDBN to view the distributionicalc
Enter row matrix of X-values XEnter row matrix of Y-values Y
Enter X probabilities PXEnter Y probabilities PY
Use array operations on matrices X, Y, PX, PY, t, u, and Pxmax = max(X)
xmax = 1040ymax = max(Y)
ymax = 800PYgX = total((u>t).*P)
PYgX = 0.5081k = [600 700 750];px = zeros(1,3);
py = zeros(1,3);for i = 1:3
px(i) = (X>=k(i))*PX';
endfor i = 1:3
py(i) = (Y>=k(i))*PY';
enddisp([px;py]')0.4131 0.2560
0.2337 0.07840.0818 0.0111 A residential College plans to raise money by selling “chances” on a board. There are two games:
Thirty chances are sold on Game 1 and fifty chances are sold on Game 2. If X and Y are the profits on the respective games, then
where are the numbers of winners on the respective games. It is reasonable to suppose binomial and binomial . It is reasonable to suppose the pair is independent, so that is independent. Determine the marginal distributions for X and Y then use icalc to obtain the joint distribution and the calculating matrices. The total profit for the College is . What is the probability the College will lose money? What is the probability the profit will be $400 or more, less than $200, between $200 and $450?
N1 = 0:30;
PN1 = ibinom(30,0.05,0:30);x = 150 - 20*N1;
[X,PX]= csort(x,PN1);
N2 = 0:50;PN2 = ibinom(50,0.2,0:50);
y = 500 - 30*N2;[Y,PY] = csort(y,PN2);icalc
Enter row matrix of X-values XEnter row matrix of Y-values Y
Enter X probabilities PXEnter Y probabilities PY
Use array operations on matrices X, Y, PX, PY, t, u, and PG = t + u;
Mlose = G<0;
Mm400 = G>= 400;
Ml200 = G<200;
M200_450 = (G>=200)&(G<=450);
Plose = total(Mlose.*P)Plose = 3.5249e-04
Pm400 = total(Mm400.*P)Pm400 = 0.1957
Pl200 = total(Ml200.*P)Pl200 =
0.0828P200_450 = total(M200_450.*P)
P200_450 = 0.8636 
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