Workers 1,...,n are currently idle. Suppose that each worker , independently, has probability p of being...
Workers 1,...,n are currently idle. Suppose that each worker , independently, has probability p of being eligible for a job and that a job is equally likely to be assigned to any of the workers that are eligible for it (if none are eligible, the job is rejected). Find the probability that the next job is assigned to worker 1.
Homework Answers
There are n workers to whom job can be assigned so number of ways of assigning next job is n. Out of these n ways, one way is for assigning job to worker 1 so the probability that the next job is assigned to worker 1 is
P = 1 / n
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Workers 1,...,n are currently idle. Suppose that each worker ,
independently, has probability p of being...
Suppose that two teams are playing a series of games each of which is independently won by team A with probability p an...
Suppose that two teams are playing a series of games each of which is independently won by team A with probability p and by team B with probability 1-p. The winner of the series is the first team to win i games. (a) If i 4, find the probability that a total of 7 games are played. (b) Find the expected number of games that are played when i 3.
Suppose that two teams are playing a series of games...
Suppose that X1, X2, ..., Xn is an iid sample, each with probability p of being...
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Suppose that there are 12 types of coupons and that each time one obtains a coupon, it is, indepe...
Suppose that there are 12 types of coupons and that each time one obtains a coupon, it is, independently of previous selections, equally likely to be any one of the 12 types. One random variable of interest is T, the number of coupons that needs to be collected until one obtains a complete set of at least one of each type. Determine the p.m.f. of T, P(T -n) based on the fact P(T- n) P(T> n-1) P(T> n)
Suppose that...
2. A department has 3 employees. By the end of any given week each worker independently...
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[20] A plant sheds X seeds, where X B(n,p).Each seed germinates with probability o independently of...
[20] A plant sheds X seeds, where X B(n,p).Each seed germinates with probability o independently of all others. Let Y number of seedlings. 5. a) Find the pmf of Y b) Determine E(Y) and Var(Y).
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4. You toss n coins, each showing heads with probability p, independently of the other tosses. Each coin that shows tails is tossed again. Let X be the total number of tails (a) What type of distribution does X have? Specify its parameter(s). (b) What is the probability mass function of the total number of tails X?
B5. (a) A factory makes 5 trucks per day, seven days per week. Each truck has probability 0.1 of ...
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A committee has nine members. There are three members that currently serve as the board's chairman...
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Suppose that two teams are playing a series of games each of which is independently won by team A with probability p and by team B with probability 1-p. The winner of the series is the first team to win i games. (a) If i 4, find the probability that a total of 7 games are played. (b) Find the expected number of games that are played when i 3.
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Suppose that X1, X2, ..., Xn is an iid sample, each with probability p of being distributed as uniform over (-1/2,1/2) and with probability 1 - p of being distributed as uniform over (a) Find the cumulative distribution function (cdf) and the probability density function (pdf) of X1 (b) Find the maximum likelihood estimator (MLE) of p. c) Find another estimator of p using the method of moments (MOM)
Suppose that there are 12 types of coupons and that each time one obtains a coupon, it is, independently of previous selections, equally likely to be any one of the 12 types. One random variable of interest is T, the number of coupons that needs to be collected until one obtains a complete set of at least one of each type. Determine the p.m.f. of T, P(T -n) based on the fact P(T- n) P(T> n-1) P(T> n)
Suppose that...
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[20] A plant sheds X seeds, where X B(n,p).Each seed germinates with probability o independently of all others. Let Y number of seedlings. 5. a) Find the pmf of Y b) Determine E(Y) and Var(Y).
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