MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Exercise #8** **EENG 3421 – Advanced Engineering Analysis** **Exercise #8** --- **Problem 1:** If \( Y \) is an exponential random variable with \( \text{Var}[Y] = 25 \), find the following: a) What is the PDF of \( Y \)? b) What is \( E[Y^2] \)? c) What is \( P[Y > 5] \)? --- **Problem 2:** If \( X \) is an Erlang \( (n, \lambda) \) random variable with parameter \( \lambda = 1/3 \) and expected value \( E[X] = 15 \), find the following: a) What is the value of the parameter \( n \)? b) What is the PDF of \( X \)? c) What is \( \text{Var}[X] \)? --- **Problem 3:** If \( Y \) is an Erlang \( (n = 2, \lambda = 2) \) random variable, find the following: a) What is \( E[Y] \)? b) What is \( \text{Var}[Y] \)? c) Find \( P[0.5 \le Y \le 1.5] \). --- **Problem 4:** If \( X \) is a continuous uniform \((-5, 5)\) random variable, find the following: a) What is the PDF of \( X \)? b) What is the CDF of \( X \)? c) What is \( E[X] \)? d) What is \( E[X^2] \)? e) What is \( E[e^X] \)? --- **Problem 5:** If \( X \) is a continuous uniform random variable with expected value \( E[X] = 7 \) and variance \( \text{Var}[X] = 3 \), then what is the PDF of \( X \)? --- **Problem 6:** Radars detect flying objects by measuring the power reflected from them. The reflected power of an aircraft can be modeled as a random variable \( Y \) with PDF: \[ f_Y(y) = \begin{cases} \frac{1}{P_0} e^{-\frac{y}{P_0}} & y \ge 0 \\ 0 & \text{otherwise} \end{cases} \
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Transcribed Image Text:**Exercise #8** **EENG 3421 – Advanced Engineering Analysis** **Exercise #8** --- **Problem 1:** If \( Y \) is an exponential random variable with \( \text{Var}[Y] = 25 \), find the following: a) What is the PDF of \( Y \)? b) What is \( E[Y^2] \)? c) What is \( P[Y > 5] \)? --- **Problem 2:** If \( X \) is an Erlang \( (n, \lambda) \) random variable with parameter \( \lambda = 1/3 \) and expected value \( E[X] = 15 \), find the following: a) What is the value of the parameter \( n \)? b) What is the PDF of \( X \)? c) What is \( \text{Var}[X] \)? --- **Problem 3:** If \( Y \) is an Erlang \( (n = 2, \lambda = 2) \) random variable, find the following: a) What is \( E[Y] \)? b) What is \( \text{Var}[Y] \)? c) Find \( P[0.5 \le Y \le 1.5] \). --- **Problem 4:** If \( X \) is a continuous uniform \((-5, 5)\) random variable, find the following: a) What is the PDF of \( X \)? b) What is the CDF of \( X \)? c) What is \( E[X] \)? d) What is \( E[X^2] \)? e) What is \( E[e^X] \)? --- **Problem 5:** If \( X \) is a continuous uniform random variable with expected value \( E[X] = 7 \) and variance \( \text{Var}[X] = 3 \), then what is the PDF of \( X \)? --- **Problem 6:** Radars detect flying objects by measuring the power reflected from them. The reflected power of an aircraft can be modeled as a random variable \( Y \) with PDF: \[ f_Y(y) = \begin{cases} \frac{1}{P_0} e^{-\frac{y}{P_0}} & y \ge 0 \\ 0 & \text{otherwise} \end{cases} \
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