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Exercise 2.1 (Sample Space and Events) The rise times (unit: min.) of a reactor for two batches are measured in an experiment. 1. Define the sample space of the experiment. 2. Define Ei where the reactor rise time of the first batch is less than 55 min. and E2 where the reactor rise time of the second batch is greater than 70 min. 3. Find E¡ U E2, E1 N E2, and E1'. 4. Are Ei and E2 mutually exclusive? 5. Are Ei and E2 exhaustive?

Exercise 2.1 (Sample Space and Events) The rise times (unit: min.) of a reactor for two batches are measured in an experiment. 1. Define the sample space of the experiment. 2. Define Ei where the reactor rise time of the first batch is less than 55 min. and E2 where the reactor rise time of the second batch is greater than 70 min. 3. Find E¡ U E2, E1 N E2, and E1'. 4. Are Ei and E2 mutually exclusive? 5. Are Ei and E2 exhaustive?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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ELABORATE Answer the following problems showing complete solution. Enclose final answers. ELABORATE Exercise 2.1 (Sample Space and Events) The rise times (unit: min.) of a reactor for two batches are measured in an experiment. 1. Define the sample space of the experiment. 2. Define Ei where the reactor rise time of the first batch is less than 55 min. and E2 where the reactor rise time of the second batch is greater than 70 min. 3. Find E¡ U E2, Ei N E2, and Ei'. 4. Are Ei and E2 mutually exclusive? 5. Are Ei and E2 exhaustive? Exercise 2.2 (Probability of Joint Event) Test results of scratch resistance and shock resistance for 100 disks of polycarbonate plastic are as follows: Shock Resistance High (B) Low (B’) Scratch Resistance High (A) Low (A') 80 6 5 Let A and A' denote the event that a disk has high scratch resistance and the event that a disk has low scratch resistance, respectively. Let B and B' denote the event that a disk has high shock resistance and the event that a disk has low shock resistance, respectively. 1. When a disk is selected at random, find the probability that both the scratch and shock resistances of the disk are high. 2. When a disk is selected at random, find the probability that the scratch or
Transcribed Image Text:ELABORATE Answer the following problems showing complete solution. Enclose final answers. ELABORATE Exercise 2.1 (Sample Space and Events) The rise times (unit: min.) of a reactor for two batches are measured in an experiment. 1. Define the sample space of the experiment. 2. Define Ei where the reactor rise time of the first batch is less than 55 min. and E2 where the reactor rise time of the second batch is greater than 70 min. 3. Find E¡ U E2, Ei N E2, and Ei'. 4. Are Ei and E2 mutually exclusive? 5. Are Ei and E2 exhaustive? Exercise 2.2 (Probability of Joint Event) Test results of scratch resistance and shock resistance for 100 disks of polycarbonate plastic are as follows: Shock Resistance High (B) Low (B’) Scratch Resistance High (A) Low (A') 80 6 5 Let A and A' denote the event that a disk has high scratch resistance and the event that a disk has low scratch resistance, respectively. Let B and B' denote the event that a disk has high shock resistance and the event that a disk has low shock resistance, respectively. 1. When a disk is selected at random, find the probability that both the scratch and shock resistances of the disk are high. 2. When a disk is selected at random, find the probability that the scratch or
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