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

# What's the point of transforming variables in engineering?

E.g. in video, (R,G,B) might be transformed to (Y,I,Q) with a 3x3 matrix multiply. Y is brightness, I,Q are color. Since we see brightness more accurately than color, we want to transmit Y with greater precision. So, we want to do probabilities on all this.

# Exercise 5.37

The number of full pairs is the floor of half the number, i.e., (1,2,3,4,5,6)->(0,1,1,2,2,3).

# Max and min of 2 uniform random variables

1. W=min(X,Y). Z=max(X,Y).
2. cdf(W), cdf(Z), pdf, mean
3. Probability that a 3rd r.v. will be bigger than the first 2.
4. Quantiles of of n r.v.
5. What is the probability that the max of 3 uniform (0,1) random variables is greater than .5?
• A: 1/8
• B: 1/3
• C: 1/2
• D: 2/3
• E: 7/8

# 5.8.3 Transformation of 2 r.v.

1. X, Y are exponential with {$\lambda=1$}.
2. What is joint pdf of (X+Y, X-Y)?