A small pond contains 50 fish, 15 of which have been tagged. Suppose that a fisherman’s...
A small pond contains 50 fish, 15 of which have been tagged. Suppose that a fisherman’s catch consists of five fish. (Assume that these five fish form a random sample of size five selected without replacement.) Let X denote the number of tagged fish that are caught.
Reconsider the fish pond problem but this time suppose that the sample is selected with replacement. A small pond contains 50 fish, 15 of which have been tagged. Suppose that a fisherman catches five fish by catching a fish, noting whether it is tagged, releasing it, and repeating until five fish have been caught. (Assume that these five fish form a random sample of size five selected with replacement.) Let X denote the number of tagged fish that are caught.
a) What is the name of the distribution of X and what is the p.m.f. of X for this example? Provide an expression for pX(x).
b) Find the probability that the fisherman’s catch will contain at most 4 tagged fish.
c) Use the appropriate expressions from section 7.9 to compute expected value of X and the variance of X.
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A small pond contains 50 fish, 15 of which have been tagged.
Suppose that a fisherman’s...
Reconsider problem 1 but suppose that the sample is selected with replacement. A small pond conta...
Reconsider problem 1 but suppose that the sample is selected with replacement. A small pond contains 30 fish, 10 of which have been tagged. Suppose that a fisherman’s catches four fish by catching a fish, noting whether it is tagged, releasing it, and repeating until four fish have been caught. (Assume that these four fish form a random sample of size four selected with replacement.) Let X denote the number of tagged fish that are caught. a) What is the...
Problem 6 A lake contains 600 fish, eighty (80) of which have been tagged by scientists....
Problem 6 A lake contains 600 fish, eighty (80) of which have been tagged by scientists. A researcher randomly catches 15 fish from the lake. a. Find a formula for the probability mass function of X, the number of fish in the researcher's sample, which are tagged b. Find the probability that none of the fish he catches are tagged c. What is the number of tagged fish he expects to catch?
A campus of Wolf City College has a fish pond. Suppose there are 20 fish in...
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A box contains ten sealed envelopes numbered 1. 10. The first three contain no money, the...
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3. Suppose a batch of 50 items contains 4 defective ones, and a sample of 5...
3. Suppose a batch of 50 items contains 4 defective ones, and a sample of 5 items is selected at random from the batch. Let X denote the number of defective items in the sample. (a) What is the name of the distribution of X? (b) Find the probability mass function for X. You may write this as a function or as a chart. If you write it as a function, also give the set of X values where the...
Suppose that in a batch of 500 components, 20 are defective and the rest are good....
Suppose that in a batch of 500 components, 20 are defective and the rest are good. A sample of 10 components is selected at random with replacement, and tested. Let X denote the number of defectives in the sample. a. What is the PMF of X? State the distribution, its parameters, and give the equation for its PMF with the correct parameters. b. What is the probability that the sample contains at least one defective component?
1: Suppose a team of biologists has been studying the Pinedale children's fishing pond. Let x...
1: Suppose a team of biologists has been studying the Pinedale children's fishing pond. Let x represent the length of a single trout taken at random from the pond. This group of biologists have determined that x has a normal distribution with mean u = 10.2 inches and standard deviation o = 1.4 inches. 1.1: What is the probability that a single trout taken at random from the pond is between 8.1 and 11.6 inches long? (5 Points) Solution 1.1:...
지 (A less tedious version of Exercise 2.1.16) An urn contains 12 chips, of which 6...
지 (A less tedious version of Exercise 2.1.16) An urn contains 12 chips, of which 6 are blue and 6 are red. Randomly select 6 chips, one at a time without replacement. Let Xbe the absolute difference between the numbers of blue and red chips that have been selected. a) Find the p.m.f. of X. Show your work. b) What value of X is most likely'? c) Find the expected value of X.
A box contains ten sealed envelopes numbered 1,..., 10. The first six contain no money, the...
A box contains ten sealed envelopes numbered 1,..., 10. The first six contain no money, the next two each contains $5, and there is a $10 bill in each of the last two. A sample of size 3 is selected with replacement (so we have a random sample), and you get the largest amount in any of the envelopes selected. If X, X, and X, denote the amounts in the selected envelopes, the statistic of interest is M = the...
It is known that 90% of all brand A external hard drives work in a satisfactory...
It is known that 90% of all brand A external hard drives work in a satisfactory manner throughout the warranty period are successes"). Suppose that n - 15 drives are randomly selected. Let X - the number of successes in the sample. The statistic X/n is the sample proportion (fraction) of successes. Obtain the sampling distribution of this statistic. (Hint: One possible value Xin is 0.2, corresponding to X - 3. What is the probability of this value (what kind...
Problem 6 A lake contains 600 fish, eighty (80) of which have been tagged by scientists. A researcher randomly catches 15 fish from the lake. a. Find a formula for the probability mass function of X, the number of fish in the researcher's sample, which are tagged b. Find the probability that none of the fish he catches are tagged c. What is the number of tagged fish he expects to catch?
A box contains ten sealed envelopes numbered 1. 10. The first three contain no money, the next five each contains $5, and there is a $10 bil in each of the last two. A sample of size 3 is selected with replacement (so we have a random sample), and you get the largest amount in any of the envelopes selected. If X, X, and X, denote the amounts in the selected envelopes, the statistic of interest is the maximum of...
3. Suppose a batch of 50 items contains 4 defective ones, and a sample of 5 items is selected at random from the batch. Let X denote the number of defective items in the sample. (a) What is the name of the distribution of X? (b) Find the probability mass function for X. You may write this as a function or as a chart. If you write it as a function, also give the set of X values where the...
1: Suppose a team of biologists has been studying the Pinedale children's fishing pond. Let x represent the length of a single trout taken at random from the pond. This group of biologists have determined that x has a normal distribution with mean u = 10.2 inches and standard deviation o = 1.4 inches. 1.1: What is the probability that a single trout taken at random from the pond is between 8.1 and 11.6 inches long? (5 Points) Solution 1.1:...
지 (A less tedious version of Exercise 2.1.16) An urn contains 12 chips, of which 6 are blue and 6 are red. Randomly select 6 chips, one at a time without replacement. Let Xbe the absolute difference between the numbers of blue and red chips that have been selected. a) Find the p.m.f. of X. Show your work. b) What value of X is most likely'? c) Find the expected value of X.
A box contains ten sealed envelopes numbered 1,..., 10. The first six contain no money, the next two each contains $5, and there is a $10 bill in each of the last two. A sample of size 3 is selected with replacement (so we have a random sample), and you get the largest amount in any of the envelopes selected. If X, X, and X, denote the amounts in the selected envelopes, the statistic of interest is M = the...
It is known that 90% of all brand A external hard drives work in a satisfactory manner throughout the warranty period are successes"). Suppose that n - 15 drives are randomly selected. Let X - the number of successes in the sample. The statistic X/n is the sample proportion (fraction) of successes. Obtain the sampling distribution of this statistic. (Hint: One possible value Xin is 0.2, corresponding to X - 3. What is the probability of this value (what kind...
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