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A production facility contains two machines that are used to rework items that are initially defective....
A production facility contains two machines that are used to rework items that are initially defective....
A production facility contains two machines that are used to rework items that are initially defective. Let X be the number of hours that the first machine is in use, and let Ybe the number of hours that the second machine is in use, on a randomly chosen day. Assume that X and Yhave joint probability density function given by 3. f(x)-| (x2 + y*) 0<x<1and 0 < y < 1 0 otherwise f. Find the conditional expectation E( 0.5)....
Two machines turn out all the products in a factory, with the first machine producing 45%...
Two machines turn out all the products in a factory, with the first machine producing 45% of the product and the second 55%. The first machine produces defective products 3% of the time and the second machine 8% of the time. (a) What is the probability that a defective part is produced at this factory given that it was made on the first machine? (b) What is the probability that a defective part is produced at this factory?
Four cutting machines are selected from a large lot of damaged machines. Each machine is inspected...
Four cutting machines are selected from a large lot of damaged machines. Each machine is inspected and classified as containing either a major or a minor defect. Let the random variables X and Y denote the number of machines with major and minor defects, respectively. Determine the range of the joint probability distribution of X and Y. a. X >= 0, Y >= 0 and X + Y = 5 b. X >= 1, Y >= 1 and X +...
7. A service facility operates with two service lines. On a randomly selected day, let X...
7. A service facility operates with two service lines. On a randomly selected day, let X be the proportion of time that the first line is in use whereas Y is the pro- portion of time that the second line is in use. Suppose that the joint probability density function for (X,Y) is f(tv) = ( +y), if 0 <r,y<1. elsewhere. (a) Compute the probability that neither line is busy more than half the time. (b) Determine whether or not...
Part 1 Suppose that 2 batteries are randomly chosen without replacement from a group of 12...
Part 1 Suppose that 2 batteries are randomly chosen without replacement from a group of 12 batteries: 3 new, 4 used (working), and 5 defective. Let the random variable X denote the number of new batteries chosen and the random variable Y denote the number of used batteries chosen. The joint distribution fxy is given in the following table: 0 12 17663/6 120/6612/66 1. Calculate P ( X 1 ,Y > 1) 2. Find the marginal probability mass function fx...
A company would like to determine the best production schedule using a manufacturing process with four...
A company would like to determine the best production schedule using a manufacturing process with four machines: W, X, Y, and Z. Each machine can be used for 2400 minutes per week. The weekly demands and the processing time on machines are shown below. Product A, 150 units/week, 6, 10, 6, 0 minutes; Product B, 90 units/week, 0, 9, 7, 8 minutes; Product C, 120 units/week, 8, 8, 7, 5 minutes; Product D, 130 units/week, 7, 0, 5, 8 minutes....
l is I unit and that of Question 3: Two machines produce a certain item. The...
l is I unit and that of Question 3: Two machines produce a certain item. The capacity per day or N Machine-2 is 2 units Let A, , be the discrete random variables for the actual daily production o i and 2, respectively. The joint probubilit y mass function is given below 0.0s o.10 0.0s 0.20 0.50 010 a. (10 points) Are X and X, independent? Justify your answer b. (10 points) Write the conditional probability mass function of Xi...
A large but sparsely populated county has two small hospitals, one at the south end of...
A large but sparsely populated county has two small hospitals, one at the south end of the county and the other at the north end. The south hospital's emergency room has four beds, whereas the north hospital's emergency room has only three beds. Let X denote the number of south beds occupied at a particular time on a given day, and let Y denote the number of north beds occupied at the same time on the same day. Suppose that...
There are two fuses in an electrical device. Let X denote the lifetime of the first...
There are two fuses in an electrical device. Let X denote the lifetime of the first fuse, and let y denote the lifetime of the second fuse (both in years). Assume the joint probability density function of X and Y is f(x,y) = (x? + 2 + 2) 0<x< 1, 0 < y < 2 a. What is the probability that both fuses last at most 4 months? b. What is the probability that the first fuse lasts less than...
There are two fuses in an electrical device. Let X denote the lifetime of the first...
There are two fuses in an electrical device. Let X denote the lifetime of the first fuse, and let y denote the lifetime of the second fuse both in years). Assume the joint probability density function of X and Yis f(x,y) – $(x +2y). 0<x<1, 0 <y<2 a. What is the probability that both uses last longer than 4 months? b. What is the probability that the second fuse lasts less than 3 months given that the first fuse last...
A production facility contains two machines that are used to rework items that are initially defective. Let X be the number of hours that the first machine is in use, and let Ybe the number of hours that the second machine is in use, on a randomly chosen day. Assume that X and Yhave joint probability density function given by 3. f(x)-| (x2 + y*) 0<x<1and 0 < y < 1 0 otherwise f. Find the conditional expectation E( 0.5)....
7. A service facility operates with two service lines. On a randomly selected day, let X be the proportion of time that the first line is in use whereas Y is the pro- portion of time that the second line is in use. Suppose that the joint probability density function for (X,Y) is f(tv) = ( +y), if 0 <r,y<1. elsewhere. (a) Compute the probability that neither line is busy more than half the time. (b) Determine whether or not...
Part 1 Suppose that 2 batteries are randomly chosen without replacement from a group of 12 batteries: 3 new, 4 used (working), and 5 defective. Let the random variable X denote the number of new batteries chosen and the random variable Y denote the number of used batteries chosen. The joint distribution fxy is given in the following table: 0 12 17663/6 120/6612/66 1. Calculate P ( X 1 ,Y > 1) 2. Find the marginal probability mass function fx...
l is I unit and that of Question 3: Two machines produce a certain item. The capacity per day or N Machine-2 is 2 units Let A, , be the discrete random variables for the actual daily production o i and 2, respectively. The joint probubilit y mass function is given below 0.0s o.10 0.0s 0.20 0.50 010 a. (10 points) Are X and X, independent? Justify your answer b. (10 points) Write the conditional probability mass function of Xi...
There are two fuses in an electrical device. Let X denote the lifetime of the first fuse, and let y denote the lifetime of the second fuse (both in years). Assume the joint probability density function of X and Y is f(x,y) = (x? + 2 + 2) 0<x< 1, 0 < y < 2 a. What is the probability that both fuses last at most 4 months? b. What is the probability that the first fuse lasts less than...
There are two fuses in an electrical device. Let X denote the lifetime of the first fuse, and let y denote the lifetime of the second fuse both in years). Assume the joint probability density function of X and Yis f(x,y) – $(x +2y). 0<x<1, 0 <y<2 a. What is the probability that both uses last longer than 4 months? b. What is the probability that the second fuse lasts less than 3 months given that the first fuse last...
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