STA104/MTH135: Probability

Homework #5: Continuous Random Variables

Due: Thursday, Oct 2

Text Problems are from Sheldon Ross, A First Course in Probability (6th edn).

• Problems (pp. 228ff)
  

  3*

  7

  14*

  17

  27

  33

  38

  *NOTE: For Problem 3b, change the limits of the function to say 0 < x < 2. For Problem 14, you may assume n>0.
• Exercises (pp. 232ff)

  25

  28*

  *NOTE: For number 28, you may assume that the cumulative distribution function given in the problem is strictly increasing (the result is still true even if this fails, but it's a little harder to show). Under what conditions on the density function is this assumption valid?
• Another Problem
  The probability density of X, the lifetime of a certain electronic device (measured in hours), is given by f(x)=200/x³ for x>10 and f(x)=0 for x<10.
  1. Find P[X>20]
  2. Find the cumulative distribution function for X.
  3. Find the hazard function for X. Is it increasing or decreasing on the interval x>10?

Good Luck!