Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
The fall 2003 midterm exam for the probability and random processes course offered by the eecs department at the university of california, berkeley. The exam consists of five questions worth 20% each, and students are required to show their work. The questions involve calculating expectations of random variables given certain conditions, finding conditional distributions, and understanding the relationship between gaussian random variables.
Typology: Exams
1 / 5
This page cannot be seen from the preview
Don't miss anything!
Department of EECS - University of California at Berkeley EECS126 - Probability and Random Processes - Fall 2003 Midterm No. 2: 11/14/
There are five questions, worth 20% each. Answer on these sheets. Show your work. Good luck.
Question 1. Let {X, Y, Z} be independent N(0, 1) random variables. a. (14%) Calculate E[3X + 5Y | 2X − Y,X + Z]. b. (6%) How does the expression change if X, Y, Z are i.i.d. N(1, 1)?
Question 2. 25%. Let X, Y be independent random variables uniformly distributed in [0, 1]. Calculate L[Y^2 | 2X + Y ].
Question 4. 20%. Given , the random variables {Xn, n 1} are i.i.d. U[0, ]. Assume that is exponentially distributed with rate . a. Find the MAP ˆn of given {X 1 ,... ,Xn}. b. Calculate E(| − ˆn|).
Question 5. 20%. Let (X, Y) be jointly Gaussian. Show that X − E[X | Y] is Gaussian and calculate its mean and variance.
