ECSE-2500, Engineering Probability, Spring 2010, Rensselaer Polytechnic Institute

# Lecture 18

# Big example mimicking homework 8.

- Homework 8 clarified.
- Let x and y be between 0 and 1.
- Let f(x,y) = c(x+y
^{2}). - Do the homework questions.

# 5.61 page 257 E[X+Y] = E[X]+E[Y]

# Example 5.27 cos, sin are uncorrelated but dependent variables.

# Conditional pmf and cdf for discrete random variables

- The textbook price example
- total probability theorem

# Conditional pdf and cdf for continuous random variables

- square and triangle examples

# Conditional expectation p268

# 5.8 p271 Functions of 2 random variables

- Z=X+Y
- f(Z) is a superposition integral
- if X, Y independent, it's a convolution