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(See Exercise 20 from "Problems on Conditional Expectation, Regression") A number X is selected randomly from the integers 1 through 100. A pairof dice is thrown X times. Let Y be the number of sevens thrown on the X tosses. Determine the distribution for Y . Determine and .
gN = 0.01*[0 ones(1,100)];gY = [5/6 1/6];gend
Do not forget zero coefficients for missing powersEnter gen fn COEFFICIENTS for gN gN
Enter gen fn COEFFICIENTS for gY gYResults are in N, PN, Y, PY, D, PD, P
May use jcalc or jcalcf on N, D, PTo view the distribution, call for gD.
EY = dot(D,PD)EY = 8.4167
P20 = (D<=20)*PD'
P20 = 0.9837 (See Exercise 21 from "Problems on Conditional Expectation, Regression") A number X is selected randomly from the integers 1 through 100. Eachof two people draw X times independently and randomly a number from 1 to 10. Let Y be the number of matches (i.e., both draw ones, both draw twos, etc.). Determine thedistribution for Y . Determine and .
gN = 0.01*[0 ones(1,100)];gY = [0.9 0.1];gend
Do not forget zero coefficients for missing powersEnter gen fn COEFFICIENTS for gN gN
Enter gen fn COEFFICIENTS for gY gYResults are in N, PN, Y, PY, D, PD, P
May use jcalc or jcalcf on N, D, PTo view the distribution, call for gD.
EY = dot(D,PD)EY = 5.0500
P10 = (D<=10)*PD'
P10 = 0.9188 Suppose the number of entries in a contest is binomial (20, 0.4). There are four questions. Let Y i be the number of questions answered correctly by the i th contestant. Suppose the Y i are iid, with common distribution
Let D be the total number of correct answers. Determine , , and .
gN = ibinom(20,0.4,0:20);
gY = 0.1*[0 2 4 3 1];
gendDo not forget zero coefficients for missing powers
Enter gen fn COEFFICIENTS for gN gNEnter gen fn COEFFICIENTS for gY gY
Results are in N, PN, Y, PY, D, PD, PMay use jcalc or jcalcf on N, D, P
To view the distribution, call for gD.ED = dot(D,PD)
ED = 18.4000VD = (D.^2)*PD' - ED^2
VD = 31.8720P1 = ((15<=D)&(D<=25))*PD'
P1 = 0.6386P2 = ((10<=D)&(D<=30))*PD'
P2 = 0.9290 Game wardens are making an aerial survey of the number of deer in a park. The number of herds to be sighted is assumed to be a random variable binomial (20, 0.5). Each herd is assumed to be from 1 to 10 in size, with probabilities
| Value | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Probability | 0.05 | 0.10 | 0.15 | 0.20 | 0.15 | 0.10 | 0.10 | 0.05 | 0.05 | 0.05 |
Let
D be the number of deer sighted under this model. Determine
for
and
.
gN = ibinom(20,0.5,0:20);
gY = 0.01*[0 5 10 15 20 15 10 10 5 5 5];
gendDo not forget zero coefficients for missing powers
Enter gen fn COEFFICIENTS for gN gNEnter gen fn COEFFICIENTS for gY gY
Results are in N, PN, Y, PY, D, PD, PMay use jcalc or jcalcf on N, D, P
To view the distribution, call for gD.k = [25 50 75 100];P = zeros(1,4);
for i = 1:4P(i) = (D<=k(i))*PD';
enddisp(P)
0.0310 0.5578 0.9725 0.9998 A supply house stocks seven popular items. The table below shows the values of the items and the probability of each being selected by a customer.
| Value | 12.50 | 25.00 | 30.50 | 40.00 | 42.50 | 50.00 | 60.00 |
| Probability | 0.10 | 0.15 | 0.20 | 0.20 | 0.15 | 0.10 | 0.10 |
Suppose the purchases of customers are iid, and the number of customers in a day is binomial (10,0.5). Determine the distribution for the total demand D .
gN = ibinom(10,0.5,0:10);
Y = [12.5 25 30.5 40 42.5 50 60];
PY = 0.01*[10 15 20 20 15 10 10];
mgdEnter gen fn COEFFICIENTS for gN gN
Enter VALUES for Y YEnter PROBABILITIES for Y PY
Values are in row matrix D; probabilities are in PD.To view the distribution, call for mD.
s = size(D)s = 1 839
M = max(D)M = 590
t = [100 150 200 250 300];
P = zeros(1,5);for i = 1:5
P(i) = (D<=t(i))*PD';
enddisp(P)
0.1012 0.3184 0.6156 0.8497 0.9614P1 = ((100<D)&(D<=200))*PD'
P1 = 0.5144 
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