Engineering Probability Class 16 Thu 2019-03-14

Source

1   Review of normal distribution

  1. Review of the normal distribution. If $\mu=0, \sigma=1$ (to keep it simple), then: $$f_N(x) = \frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}} $$
  2. Show that $\int_{-\infty}^{\infty} f(x) dx =1$. This is example 4.21 on page 168.
  3. Iclicker: Consider a normal r.v. with $\mu=500, \sigma=100$. What is the probability of being in the interval [400,600]? Page 169 might be useful.
    1. .02
    2. .16
    3. .48
    4. .68
    5. .84
  4. Iclicker. Repeat that question for the interval [500,700].
  5. Iclicker. Repeat that question for the interval [0,300].

2   Chapter 5, Two Random Variables

  1. See intro I did in last class.
  2. Today's reading: Chapter 5, page 233-242.
  3. Review: An outcome is a result of a random experiment. It need not be a number. They are selected from the sample space. A random variable is a function mapping an outcome to a real number. An event is an interesting set of outcomes.
  4. Example 5.3 on page 235. There's no calculation here, but this topic is used for several future problems.
  5. Example 5.5 on page 238. We saw this on Monday.
  6. Example 5.6 on page 240. Easy, look at it yourself.
  7. Example 5.7 on page 241. Easy, look at it yourself.
  8. Example 5.8 on page 242. Easy, look at it yourself.
  9. Example 5.9 on page 242.
  10. Example 5.11 on page 245. What is f(x,y)?
  11. Cdf of mixed continuous - discrete random variables: section 5.3.1 on page 247. The input signal X is 1 or -1. It is perturbed by noise N that is U[-2,2] to give the output Y.. What is P[X=1|Y<=0]?
  12. Example 5.14 on page 247.
  13. Example 5.16 on page 252.