Computer chips often contain surface imperfections. For a certain type of computer chip,the probability mass function of the number of defects X is presented in the following table.234p(x)0.40.30.150.100.05Find P(X < 2).a.Find P(X > 1).b.Find Hx-C.Find o.d.

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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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A Consider that the variables X and Y have the following joint probability distribution. 1. 3. 0.05 0.05 0.00 0.05 0.10 0.20 0.10 0.35 0.10 (a) Find the marginal distribution of X (b) Find the marginal distribution of Y (c) Determine if X and Y are statistically independent. (d) Find P(Y = 1|X = 3).
Answer parts 1 and 2 of the problem below.
DHL usually gives its customer a 60-minute window in which it expects home deliveries to be delivered. An independent consultant estimates that the final delivery time within the window is a delivery that follows the following condensation function:a. Draw the density function of the event. b. What is the expected value of the transaction? c. What is the variance of the event?
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
Chapters: Normal and Exponential random variables. Q: Let X be an exponential random variable with rate 1. If a and b are positive numbers, then P(X > a + b|X > b) = P(X > a). a. Explain why this is called the memoryless property b. Show that for an exponential rv X with rate 1, P(X > a) = e-ad.
(i) Attempt the following questions. Show all necessary steps. Read the questions carefully. (ii) Any copied material from internet or your class fellows will get you ZERO marks. Q. 1 Let X be the number of bugs in the first draft of a piece of software, and let Y be the number of bugs remaining in the second draft of the same software. Their joint probability mass function is given by the following table: Y 0. 1 3 0. 0.03 0.14 0.09 0.08 1 0.05 0.10 K 0.04 0.04 0.09 0.08 0.09 (i) Obtain K so that it is the joint probability mass function; (ii) Find cumulative distribution function Fyy (x, y); (iii) Find the following probabilities using cdf obtained above (a) P(X 4), (c) P(X + Y > 3), (e) P(X < 3,Y < 2) 21

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Computer chips often contain surface imperfections. For a certain type of computer chip, the probability mass function of the number of defects X is presented in the following table. 2 3 4 p(x) 0.4 0.3 0.15 0.10 0.05 Find P(X < 2). a. Find P(X > 1). b. Find Hx- C. Find o. d.