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What is P(150 < X1 + X2 + X3 526. 2. Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent normal random variables with expected values µ1, 42, and µ3 and variances ī, º2, and 3, respectively. a. If u= µ2 = µ3 = 65 and , calculate P(X1 + X2+ X3 < 210). P(62<ÃS68). b. Using the µ's and af's given in part (a), calculate P(X2 59) and

What is P(150 < X1 + X2 + X3 526. 2. Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent normal random variables with expected values µ1, 42, and µ3 and variances ī, º2, and 3, respectively. a. If u= µ2 = µ3 = 65 and , calculate P(X1 + X2+ X3 < 210). P(62<ÃS68). b. Using the µ's and af's given in part (a), calculate P(X2 59) and

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Problem 2: Analysis of Repair Task Times** Let \(X_1, X_2, \text{ and } X_3\) represent the times necessary to perform three successive repair tasks at a certain service facility. Assume they are independent normal random variables with expected values \(\mu_1, \mu_2, \text{ and } \mu_3\) and variances \(\sigma_1^2, \sigma_2^2, \text{ and } \sigma_3^2\), respectively. a. Given \(\mu = \mu_2 = \mu_3 = 65\) and \(\sigma_1^2 = \sigma_2^2 = \sigma_3^2 = 20\), calculate \(P(X_1 + X_2 + X_3 \leq 210)\). What is \(P(150 \leq X_1 + X_2 + X_3 \leq 210)\)? b. Using the \(\mu_i\)'s and \(\sigma_i\)'s given in part (a), calculate \(P\left( \overline{X} \geq 59 \right)\) and \(P(62 \leq \overline{X} \leq 68)\). c. Using the \(\mu_i\)'s and \(\sigma_i\)'s given in part (a), calculate \(P(-10 \leq X_1 - .5X_2 - .5X_3 \leq 5)\). d. If \(\mu_1 = 40, \mu_2 = 50, \mu_3 = 60, \sigma_1^2 = 10, \sigma_2^2 = 12, \text{ and } \sigma_3^2 = 14\), calculate \(P(X_1 + X_2 + X_3 \leq 160)\) and \(P(X_1 + X_2 \geq 2X_3)\). **Diagram Explanation**: This problem does not contain graphs or diagrams that require explanation. It is presented as a series of mathematical and statistical questions concerning the calculation of probabilities and expectations of normal random variables. Each of these problems involves understanding and application of properties of normal distributions and their combinations.
Transcribed Image Text:**Problem 2: Analysis of Repair Task Times** Let \(X_1, X_2, \text{ and } X_3\) represent the times necessary to perform three successive repair tasks at a certain service facility. Assume they are independent normal random variables with expected values \(\mu_1, \mu_2, \text{ and } \mu_3\) and variances \(\sigma_1^2, \sigma_2^2, \text{ and } \sigma_3^2\), respectively. a. Given \(\mu = \mu_2 = \mu_3 = 65\) and \(\sigma_1^2 = \sigma_2^2 = \sigma_3^2 = 20\), calculate \(P(X_1 + X_2 + X_3 \leq 210)\). What is \(P(150 \leq X_1 + X_2 + X_3 \leq 210)\)? b. Using the \(\mu_i\)'s and \(\sigma_i\)'s given in part (a), calculate \(P\left( \overline{X} \geq 59 \right)\) and \(P(62 \leq \overline{X} \leq 68)\). c. Using the \(\mu_i\)'s and \(\sigma_i\)'s given in part (a), calculate \(P(-10 \leq X_1 - .5X_2 - .5X_3 \leq 5)\). d. If \(\mu_1 = 40, \mu_2 = 50, \mu_3 = 60, \sigma_1^2 = 10, \sigma_2^2 = 12, \text{ and } \sigma_3^2 = 14\), calculate \(P(X_1 + X_2 + X_3 \leq 160)\) and \(P(X_1 + X_2 \geq 2X_3)\). **Diagram Explanation**: This problem does not contain graphs or diagrams that require explanation. It is presented as a series of mathematical and statistical questions concerning the calculation of probabilities and expectations of normal random variables. Each of these problems involves understanding and application of properties of normal distributions and their combinations.
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