Continuous Random Variables Reading: Chapter 3.1 – 3.8 Homework: 3.1.2, 3.2.1, 3.2.4, 3.3.2, 3.3.7, 3.4.4, 3.4.5, 3.4.9, 3.5.3., 3.5.6, 3.6.1, 3.6.6, 3.7.1, 3.7.3, 3.7.11, 3.8.1.

Cumulative Distribution Function CDF of a random variable X is: FX(x) = P[X≤x] X is a continuous random variable if FX(x) is continuous. (the range of X contains a continuous interval) Example: X: a random integer between 0 and 4. SX={0,1,2,3,4} PX(x) = 0.2 for x=0,1,2,3,4 and 0 otherwise FX(x) is an non-decreasing piece-wise constant function that is not continuous at x=0,1,2,3,4

Y: a random real number between 0 and 4.

SY =[0,4] is a continuous region, not a countable set.  0  FY[y] = P[Y≤y] = ? FY ( y ) =  y / 4 PY[Y=y] = ?

 1 

G. Qu

ENEE 324 Engineering Probability

y4 2

1

Properties of CDF Theorem 3.1: for any random variable X FX(-∞) = 0, FX(∞) = 1 FX(x) = 0 for x