Homework #8
EE 364: Spring 2026
Assigned: 12 March
Due: Thursday, 19 March at 16:00
BrightSpace Assignment: Homework 8
Write your solutions to these homework problems. Submit your work to BrightSpace by the due date. Show all work and box answers where appropriate. Do not guess.
Problem 0
Daily derivation #8
Derive the pdf for \(Y = g(X)\) if \(g(x)\) is 1-to-1.
Problem 1
Random variable \(Y = e^X\). Find the pdf of \(Y\) when \(X\) is a Gaussian random variable – in this case \(Y\) is said to be a lognormal random variable. Plot the pdf and cdf of \(Y\) when \(X\) is zero-mean with variance \(\frac{1}{8}\). Repeat with variance 8.
Problem 2
Let \(Y = \alpha \tan \left( \pi X \right)\), where \(X\) is uniformly distributed in the interval \([-1, 1]\). Determine the pdf \(f_Y(y)\) and identify \(Y\) as one of the BEG-CUP random variables.
Problem 3
Let a radius be given by the random variable X as: \[f_X(x) = \begin{cases} c x \left( 1 - x^2\right) & 0 \le x \le 1 \\ 0 & \textrm{else} \end{cases}\]
Find the pdf of the area covered by a disc with radius \(X\).
Find the pdf of the volume of a sphere with radius \(X\).
Problem 4
A voltage \(X\) is a Gaussian random variable with mean 1 and variance 2. Find the pdf of the power dissipated by an \(R\)-\(\Omega\) resistor \(P = R X^2\).