2. A bank operates both a drive-up facility and a walk-up window. On arandomly selected day, let X = the proportion of time that the drive-up facilityis in use (at least one customer is being served or waiting to be served) and Y= the proportion of the time that the walk-up window is in use. Then the setof possible values for (X, Y) is the rectangleD = {(x, y): 0 ≤ x ≤ 1,0 ≤ y ≤ 1}. Suppose the joint probability densityfunction of (X, Y) is given by:fx,y(x,y) = { / (x + y ² )²²(x + y²) 0≤x≤ 1,0 ≤ y ≤ 1Otherwise0(a) Show that fx,y is legitimate(b) Find the probability that neither facility is busy more than one-quarter ofthe time.(c) Find fx and fy, the marginal probability density function of X and Yrespectively.(d) Construct the conditional probability density function of Y given thatX=0.8.(e) Evaluate the probability that the walk-up facility is busy at most half of thetime given that X=0.8(f) Calculate the expected proportion of the time that the walk-up facility isbusy given that X=0.8Tutor: Takembo Clovis (L)

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Answered: 2. A bank operates both a drive-up…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Answer for section iv)
The following table indicates the unit prices (in Rands) and quantities of three goods purchased every month by a small restaurant for the years 2023 and 2024. GOOD 2023 2024 Unit Price (p0) Quantity (q0)) Unit Price (p1) Quantity (q1) Milk R12.60 2555 R12.85 2705 Eggs R11.00 114 R14.00 107 Flour R65.00 350 R68.50 400 Q.3.1 Using 2023 as the base year, compute the price relative in 2024 for milk and eggs. Interpret your answers. Q.3.2 Using 2023 as the base year, compute the Laspeyres price index for all of the goods for 2024. Interpret your answer. Q.3.3 Using 2023 as the base year, compute the Paasche price index for all of the goods for 2024. Interpret your answer.
3 The ordering and trans Portation cost C (in hundreds of dollars) for an automobi le dealership is modeled by C=6 + where X is the number of automobiles ordered. tind the Open interuals on which the cost is increasing or decreasing.
Q3) The average annual rainfall at (5) rain gauge stations in the catchment is as follows: ST Station Average Annual Rainfall (mm) P 2400 2332 2431 2207 2231 The rainfall at Station(P) was not available for the year (1996) .The rainfall observe at the other station for (1996) was as follows: PQ Station Rainfall (mm) R ? 2113 2200 2028 2095 т Estimate that rainfall at (P) During (1996).
A farmer wants to decide which of the three crops he should plant on his 100-acre farm. The profit from each is dependent on the rainfall during the growing seasons. The farmer has categorized the amount of rainfall as high, medium, low. His estimated profit for each is shown in the table. If the farmer wishes to plant only one crop, decide which will be his choice using the EMV rule, prove your judgement by comparing the EMV of each crop. (Indicate the EMV in each crop, comparison and the right choice).
The data below are the temperatures on randomly chosen days during the summer and the number of employee absences at a local company on those days. Test the claim, at the α = 0.05 level of significance, that a linear relation exists between the two variables, Apply classical and traditional approaches. Show step1-step3.
I can identify functions as linear or non-linear. Classify the following representations as "linear" or "non- linear" by recording the letter in the appropriate column on your recording sheet. A. В. с. y 4. -11.2 y = x3 8 -26.4 12 -4 1.6 16 -56.8 D. E. F. y 1. y = -X 10 y : 3 8. 24 7 48 G. Н. I. y 20 y = 2. 10 15 5. 4. OManeuvering the Middie LLC, 20 16 4.
conditions of both the districts with reference to these two causes of death. Assume The following are the information about the number of persons who are affected by Diabetes and Lung Cancer and the number of persons died due to Find the 1llness specific death rates for the two districts. Also, compare health District A District B No. of Persons No. of Persons Cause of Death Affected Died Affected Died 20000 325 22000 400 Diabetes 19500 300 21225 380 Lung Cancer la person affected by Diabetes is not affected by Lung Cancer and vice-versa.
The set of functions (4X ,4*+3) is O a. Non Linear O b. Linearly Independent O c. Linearly Dependent O d. Linear
Teachers get courses assigned to teach each semester. For each instructor, there are the courses that the instructor can teach based on the skill set of the instructor, and there are courses that the teacher would rather teach all the time, closer to their specialization. To be able to teach in any department, a teacher must be able to teach more than the favorite courses. Let X denote the proportion of teachers who teach the whole spectrum of courses taught in a department, and Y the proportion of teachers who teach the courses they specialize in. Let X and Y have the joint density function : f(x,y)=2(x+y),0<y<x<1 (a) Given that 10% of the teachers teach the whole spectrum of courses, what is the probability that fewer than 5% teach their favorite courses? (b) What is the expected percentage of teachers teaching their favorite courses when the proportion of teaching the whole spectrum is 0.7?
1. .3 For what value of x does the function g(x) - 2x strictly convex? A. X 2 В. C. X -2 D.

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