Week 7. Continuous Random Variable-I

Class Outline

Compare and Contrast with discrete random variable

• From Discrete Uniform DU(K) to Uniform, U(0,1)
• pmf vs pdf
• Relation between the distribution function F(x) and pdf f(x) of a continous random variable
  $$F′(x)=f(x).$$
• pdf is not a probability but a funciton/tool for computing probability. Specifically,
  $$f(x)\neq P(X=x)$$
  and
  $$P(a≤X≤b)=\int_a^bf(x)\ dx.$$
• Uniform U(0,1)
• Exponential random variable $Exp(\lambda)$
• Normal random variable $N(\mu, \sigma^2).$ (if time permits)

Homework 4

Textbook Sec 58 (Page 68): 5.1–5.6. To be discussed in class 11/1.