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: 1,6)= y20 otherwise where PO> 0 is some constant. The aircraft is correctly identified by the radar if the reflected power of the aircraft is larger than its average value. What is the probability P[C] that an aircraft is correctly identified?
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: 1,6)= y20 otherwise where PO> 0 is some constant. The aircraft is correctly identified by the radar if the reflected power of the aircraft is larger than its average value. What is the probability P[C] that an aircraft is correctly identified?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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![# 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 \(\text{E}[Y^2]\)?
c) What is \(\text{P}[Y > 5]\)?
### Problem 2
If \( X \) is an Erlang \( (n, \lambda) \) random variable with parameter \( \lambda = 1/3 \) and expected value \(\text{E}[X] = 15\), 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 \(\text{E}[Y]\)?
b) What is \(\text{Var}[Y]\)?
c) Find \(\text{P}[0.5 \leq Y < 1.5]\).
### 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 \(\text{E}[X^2]\)?
d) What is \(\text{E}[X]\)?
e) What is \(\text{E}[e^X]\)?
### Problem 5
If \( X \) is a continuous uniform random variable with expected value \(\text{E}[X] = 7\) 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 \geq 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe36fb7f7-6381-4add-b52b-9085dfd27844%2F8ec68a4c-ed78-4753-bcb7-d8292df4bf9d%2F8iszzqb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# 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 \(\text{E}[Y^2]\)?
c) What is \(\text{P}[Y > 5]\)?
### Problem 2
If \( X \) is an Erlang \( (n, \lambda) \) random variable with parameter \( \lambda = 1/3 \) and expected value \(\text{E}[X] = 15\), 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 \(\text{E}[Y]\)?
b) What is \(\text{Var}[Y]\)?
c) Find \(\text{P}[0.5 \leq Y < 1.5]\).
### 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 \(\text{E}[X^2]\)?
d) What is \(\text{E}[X]\)?
e) What is \(\text{E}[e^X]\)?
### Problem 5
If \( X \) is a continuous uniform random variable with expected value \(\text{E}[X] = 7\) 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 \geq 0
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