10/13/2021

Chapter 5

• Example - Let T be the time we have to wait until the next bus comes along. Assume that the next bus arrives at a time which is "equally likely" to be anywhere in the next 10 minutes.
  • What is the p.d.f of T?
• Definition of cumulative distribution function
• Return to example above.
  • What is the c.d.f. of T?
• Properties of F(t):
• The probability of being in an interval (a, b] is obtained from the c.d.f. as a difference: F(b) - F(a).
• Since F(t) is a probability, 0 <= F(t) <=1.
• Look at limit values.
• F(t) is nondecreasing.
• If T is a continuous random variable, then F(t) is continuous for all t and F'(t) exists, except possibly for finitely many values of t.
• Relationship between a p.d.f and a c.d.f.
• Transformation of Variables (Technique #1 - Using the c.d.f.)
• Continuous Probability Distributions
  • Uniform
    • Uniform(0, 1)
    • Uniform(0,10)
    • Finding the mean of uniform distributions
    • General discussion about finding the mean of a continuous R.V.
  • Normal
• Continuous Probability Distributions with R - (see ContinuousDist.R in our Google Drive folder)
  • Uniform
  • Normal

In class exercises - use RStudio to solve the problems below

• 5.13, 5.15, 5.19, 5.38(a)

Please read Chapter 5 for class on Wednesday.