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(See Exercises 3 and 4 from "Problems on Random Variables and Probabilities"). 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 and plot the distribution function F X .
T = [1 3 2 3 4 2 1 3 5 2];pc = 0.01*[8 13 6 9 14 11 12 7 11 9];[X,PX] = csort(T,pc);ddbn
Enter row matrix of VALUES XEnter row matrix of PROBABILITIES PX % See MATLAB plot (See Exercise 6 from "Problems on Random Variables and Probabilities"). 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 and plot the distribution function for X .
T = [3.5 5 3.5 7.5 5 5 3.5 7.5];pc = 0.01*[10 15 15 20 10 5 10 15];[X,PX] = csort(T,pc);ddbn
Enter row matrix of VALUES XEnter row matrix of PROBABILITIES PX % See MATLAB plot (See Exercise 12 from "Problems on Random Variables and Probabilities"). The class has minterm probabilities
Determine and plot the distribution function for the random variable , which counts the number of the events which occur on a trial.
npr06_12 Minterm probabilities in pm, coefficients in c
T = sum(mintable(4)); % Alternate solution. See
Exercise 12 from "Problems on Random Variables and Probabilities"
[X,PX]= csort(T,pm);
ddbnEnter row matrix of VALUES X
Enter row matrix of PROBABILITIES PX % See MATLAB plot Suppose a is a ten digit number. A wheel turns up the digits 0 through 9 with equal probability on each spin. On ten spins what is the probabilityof matching, in order, k or more of the ten digits in a , ? Assume the initial digit may be zero.
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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. What is the probability that k fires are started, ?
P = ibinom(127,0.0083,0:3) P = 0.3470 0.3688 0.1945 0.0678
A manufacturing plant has 350 special lamps on its production lines. On any day, each lamp could fail with probability . These lamps are critical, and must be replaced as quickly as possible. It takes about one hour toreplace a lamp, once it has failed. What is the probability that on any day the loss of production time due to lamp failaures is k or fewer hours,
P = 1 - cbinom(350,0.0017,1:6)
= 0.5513 0.8799 0.9775 0.9968 0.9996 1.0000 Two hundred persons buy tickets for a drawing. Each ticket has probability 0.008 of winning. What is the probability of k or fewer winners,
P = 1 - cbinom(200,0.008,3:5) = 0.7838 0.9220 0.9768
Two coins are flipped twenty times. What is the probability the results match (both heads or both tails) k times, ?
P = ibinom(20,1/2,0:20)
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