3. Computer chips often contain surface imperfections. For a certain type of computer chips, the probability mass function of the number of defects X is presented in the following table. x 0 1 2 3 4 5 P(x) 0.28 0.23 0.18.15 0.13 0.03 a) Find P(X ≤2). b) Find P(X> 1). c) Find the mean number of defects, μ d) Find the variance of the number of defects, o²
3. Computer chips often contain surface imperfections. For a certain type of computer chips, the probability mass function of the number of defects X is presented in the following table. x 0 1 2 3 4 5 P(x) 0.28 0.23 0.18.15 0.13 0.03 a) Find P(X ≤2). b) Find P(X> 1). c) Find the mean number of defects, μ d) Find the variance of the number of defects, o²
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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
Transcribed Image Text:**Computer Chips and Surface Imperfections**
Computer chips often contain surface imperfections. For a certain type of computer chips, the probability mass function of the number of defects \( X \) is presented in the following table:
| \( x \) | 0 | 1 | 2 | 3 | 4 | 5 |
|---------|-----|-----|-----|-----|-----|-----|
| \( P(x) \) | 0.28 | 0.23 | 0.18 | 0.15 | 0.13 | 0.03 |
**Tasks:**
a) **Find \( P(X \leq 2) \).**
*Compute the probability that the number of defects is 2 or less.*
b) **Find \( P(X > 1) \).**
*Compute the probability that the number of defects is greater than 1.*
c) **Find the mean number of defects, \( \mu_x \).**
*Calculate the expected value or average number of defects.*
d) **Find the variance of the number of defects, \( \sigma^2 \).**
*Calculate how much the number of defects varies from the mean number of defects.*
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