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(See Exercise 1 from "Problems on Distribution and Density Functions", m-file npr07_01.m ). The class is a partition. Random variable X has values on C 1 through C 10 , respectively, with probabilities 0.08, 0.13, 0.06, 0.09, 0.14, 0.11, 0.12, 0.07, 0.11, 0.09.Determine .
% file
npr07_01.m % Data for
Exercise 1 from "Problems on Distribution and Density Functions"
T = [1 3 2 3 4 2 1 3 5 2];
pc = 0.01*[ 8 13 6 9 14 11 12 7 11 9];
disp('Data are in T and pc')npr07_01
Data are in T and pcEX = T*pc'
EX = 2.7000[X,PX] = csort(T,pc); % Alternate using X, PXex = X*PX'
ex = 2.7000 (See Exercise 2 from "Problems on Distribution and Density Functions", m-file npr07_02.m ). A store has eight items for sale. The prices are $3.50, $5.00, $3.50, $7.50, $5.00, $5.00, $3.50, and $7.50, respectively.A customer comes in. She purchases one of the items with probabilities 0.10, 0.15, 0.15, 0.20, 0.10 0.05, 0.10 0.15. Therandom variable expressing the amount of her purchase may be written
Determine the expection of the value of her purchase.
% file
npr07_02.m % Data for
Exercise 2 from "Problems on Distribution and Density Functions"
T = [3.5 5.0 3.5 7.5 5.0 5.0 3.5 7.5];
pc = 0.01*[10 15 15 20 10 5 10 15];
disp('Data are in T, pc')npr07_02
Data are in T, pcEX = T*pc'
EX = 5.3500[X,PX] = csort(T,pc);ex = X*PX'
ex = 5.3500 (See Exercise 12 from "Problems on Random Variables and Probabilities", and Exercise 3 from "Problems on Distribution and Density Functions," m-file npr06_12.m ). The class has minterm probabilities
Determine the mathematical expection for the random variable , which counts the number of the events which occur on a trial.
% file
npr06_12.m % Data for
Exercise 12 from "Problems on Random Variables and Probabilities"
pm = 0.001*[5 7 6 8 9 14 22 33 21 32 50 75 86 129 201 302];
c = [1 1 1 1 0];
disp('Minterm probabilities in pm, coefficients in c')npr06_12
Minterm probabilities in pm, coefficients in ccanonic
Enter row vector of coefficients cEnter row vector of minterm probabilities pm
Use row matrices X and PX for calculationsCall for XDBN to view the distribution
EX = X*PX'EX = 2.9890
T = sum(mintable(4));[x,px] = csort(T,pm);ex = x*px
ex = 2.9890 (See Exercise 5 from "Problems on Distribution and Density Functions"). In a thunderstorm in a national park there are 127 lightning strikes. Experience shows that the probability of of a lightning strike starting a fire is about0.0083. Determine the expected number of fires.
binomial (127, 0.0083).
(See Exercise 8 from "Problems on Distribution and Density Functions"). Two coins are flipped twenty times. Let X be the number of matches (both heads or both tails). Determine .
binomial (20, 1/2). .
(See Exercise 12 from "Problems on Distribution and Density Functions"). A residential College plans to raise money by selling “chances” on a board. Fifty chances are sold. A player pays $10 to play; he or she wins $30with probability . The profit to the College is
Determine the expected profit .
binomial (50, 0.2). . .
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