Do ##6 # EENG 3421 – Advanced Engineering Analysis## Exercise #8### Problem 1If \( Y \) 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 2If \( X \) 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 3If \( Y \) 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 4If \( X \) 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 5If \( X \) 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 6Radars 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

From the given information, Let Y be the reflected power of an aircraft having the pdf,…

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?