The employees of a subsidiary that does asbestos cleanup are being tested for indications of asbestos in their lungs. The firm is asked to send four employees who have positive indications of asbestos on to a medical center for further testing. Suppose 40% of the employees have asbestos in their lungs. Let Xi be the number of employees who are screen-tested to find one who has positive indications of asbestos in his/her lungs. a. Let Y be the total number of employees tested to find four with positive asbestos in their lungs. Define Y as a function of X. Using the MGF technique, find the probability distribution of Y. b. Concerned with the cost of screening test; Lee Hu Kay would like to know the maximum number of employees tested to find one who has positive indications of asbestos in his/her lungs (Z). Given X₁, X₂, X₂ and X4, derive the distribution function of Z. c. Suppose the cost of each screening test is 5000 pesos. Let W be the total cost incurred by the company to find one employee who has positive indications of asbestos in his/her lungs. Find the distribution function of W using the CDF technique.

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The employees of a subsidiary that does asbestos cleanup are being tested for
indications of asbestos in their lungs. The firm is asked to send four employees who
have positive indications of asbestos on to a medical center for further testing.
Suppose 40% of the employees have asbestos in their lungs. Let Xi be the number of
employees who are screen-tested to find one who has positive indications of asbestos
in his/her lungs.
a. Let Y be the total number of employees tested to find four with positive asbestos in
their lungs. Define Y as a function of X. Using the MGF technique, find the probability
distribution of Y.
b. Concerned with the cost of screening test; Lee Hu Kay would like to know the
maximum number of employees tested to find one who has positive indications of
asbestos in his/her lungs (Z). Given X₁, X₂, X₂ and X4, derive the distribution function of
Z.
c. Suppose the cost of each screening test is 5000 pesos. Let W be the total cost
incurred by the company to find one employee who has positive indications of
asbestos in his/her lungs. Find the distribution function of W using the CDF technique.
Transcribed Image Text:The employees of a subsidiary that does asbestos cleanup are being tested for indications of asbestos in their lungs. The firm is asked to send four employees who have positive indications of asbestos on to a medical center for further testing. Suppose 40% of the employees have asbestos in their lungs. Let Xi be the number of employees who are screen-tested to find one who has positive indications of asbestos in his/her lungs. a. Let Y be the total number of employees tested to find four with positive asbestos in their lungs. Define Y as a function of X. Using the MGF technique, find the probability distribution of Y. b. Concerned with the cost of screening test; Lee Hu Kay would like to know the maximum number of employees tested to find one who has positive indications of asbestos in his/her lungs (Z). Given X₁, X₂, X₂ and X4, derive the distribution function of Z. c. Suppose the cost of each screening test is 5000 pesos. Let W be the total cost incurred by the company to find one employee who has positive indications of asbestos in his/her lungs. Find the distribution function of W using the CDF technique.
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