A stockroom currently has 30 components of a certain type, of which 9 were provided by supplier 1, 7 by supplier 2, and 14 by supplier 3.Six of these are to be randomly selected for a particular assembly. Let X = the number of supplier 1's components selected, Y = the numberof supplier 2's components selected, and p(x, y) denote the joint pmf of X and Y.(a) What is p(2, 1)? [Hint: Each sample of size 6 is equally likely to be selected. Therefore,p(2, 1) = (number of outcomes with X = 2 and Y = 1)/(total number of outcomes). Now use the product rule for counting to obtain thenumerator and denominator.] (Round your answer to five decimal places.)Р(2, 1) %3D(b) Using the logic of part (a), obtain p(x, y). (This can be thought of as a multivariate hypergeometric distribution-sampling withoutreplacement from a finite population consisting of more than two categories. Round your answers to five decimal places.)p(x, y)2.3412Y 34

A discrete random variable is a variable whose values can be obtained by counting. Though, the…

Answered: A stockroom currently has 30 components…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...

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1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2
In a comparative study of two new drugs, A and B, 350 patients were treated with drug A, and 225 patients were treated with drug B. (The two treatment groups were randomly and independently chosen.) It was found that 241 patients were cured using drug A and 157 patients were cured using drug B. Let p1 be the proportion of the population of all patients who are cured using drug A, and let p2 be the proportion of the population of all patients who are cured using drug B. Find a 90% confidence interval for −p1p2 . Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your responses to at least three decimal places. (If necessary, consult a list of formulas.) What is the lower limit of the 90% confidence interval? What is the upper limit of the 90% confidence interval?
A certain market has both an express checkout line and a superexpress checkout line. Let X1 denote the number of customers in line at the express checkout at a particular time of day, and let X2 denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X1 and X2 is as given in the accompanying table. x2 0 1 2 3 x1 0 0.09 0.07 0.04 0.00 1 0.05 0.15 0.05 0.04 2 0.05 0.03 0.10 0.06 3 0.01 0.02 0.04 0.07 4 0.00 0.02 0.05 0.06 (a) What is P(X1 = 1, X2 = 1), that is, the probability that there is exactly one customer in each line?P(X1 = 1, X2 = 1) = (b) What is P(X1 = X2), that is, the probability that the numbers of customers in the two lines are identical?P(X1 = X2) = (c) Let A denote the event that there are at least two more customers in one line than in the other line. Express A in terms of X1 and X2. A = {X1 ≥ 2…
Human blood types are classified by three gene forms A, B, and O. Blood types AA, BB, and OO are homozygous, and blood types AB, AO, and BO are heterozygous. If p, q, and r represent the proportions of the three gene forms to the popula-tion, respectively, then the Hardy-Weinberg Law asserts that the proportion Q of heterozygous persons in any specific population is modeled by Q(p, q, r) = 2(pq + pr + qr), subject to p + q + r = 1. Find the maximum value of Q.
If X1, X2, ... , Xn constitute a random sample of size nfrom a geometric population, show that Y = X1 + X2 +···+ Xn is a sufficient estimator of the parameter θ.
In a clinical study, a random sample of 540 participants agree to have their blood drawn, which is to be examined for the presence of antibodies against a certain contagious disease. It is found in 22% of the blood samples, which experimenters hope to extrapolate to the general population. From this random sample, 10 participants' blood samples are selected at random. If X is the number of samples out of the 10 who have these antibodies, what can we say about X? A. The sample size is not large enough for us to approximate X using a normal distribution B.The expected value of X is 22 C. X can be approximated using a normal distribution in lieu of a binomial distribution D. X has a sampling distribution that is normal
A manufacturing company employs two inspecting devices to sample a fraction of their output for quality control purposes. The first inspection monitor is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Determine the following. 1) fxy(x,y) 2) fx (x)3) fY|2 4) E(x)Show all work
From historical data at a local restaurant indicate that 60% of customers order coffee, 15% order soft drinks, and the remaining order water. The owner of the restaurant is planning on opening a new restaurant for the purpose of stocking enough of various drinks, wants to know if the proportions are the same for his new restaurant as they were for his original restaurant. In a sample of 1000 customers at the new restaurant, 550 ordered coffee, 190 order soft drinks, and the remaining simply wanted water. At the 5% level of significance, does it appear the proportions have changed?
Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. a) State the appropriate null and alternate hypotheses. b) Find the P-value. c) Should a change be made?
Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 149 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. P-value?
At the Blood Bank, they know that O+ blood is the most common blood type and that 40% of the people are known to have O+ blood. Blood type A- is a very scarce blood type and only 6% of the people have A- blood. Half of the people have blood type A or B. Let: X= number of people who have blood type O+ Y= number of people who have blood type A- Z= number of people who have blood type A or B a) Consider a random sample of n=9 people who donated blood over the past three months. The expected number of people with blood type O+ is and the expected number of people with blood type A- is Calculate the following probabilities: P(X=5)= __________ Round your answer to 4 decimal places. P(X>2)= __________ Round your answer to 4 decimal places. b) Consider a random sample of n=40 people who donated blood over the past three months. Use the relevant probability function of Y to calculate the probability that 2 people in the random sample will have type A- blood. ________…
From historical data at a local restaurant indicate that 60% of the customers order coffee, 15% ordersoft drinks, and the remaining order water. The owner of the restaurant is planning on opening a newrestaurant and for purposes of stocking enough of the various drinks, wants to know if the proportionsare the same for his new restaurant as they were for his original restaurant. In a sample of 1000customers at the new restaurant, 550 ordered coffee, 190 ordered soft drinks, and the remaining simplywanted water. At the 5% level of significance, does it appear the proportions have changed?

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