Chapter 5 Joint Probability Distributions and Random Samples

Joint p.m.f. for two DISCRETE random variables

Def. Let x and y be two discrete random variables defined on the sample space of an experiment. The joint probability mass functions p(x,y) is defined for each pair of numbers (x,y) by: p (x,y) = p (X = x, and Y = y) = fxy (x,y) Let A be any set consisting of pairs of (x,y) values. Then the probability P [(x, y) A] is obtained by summing the joint pmf over pairs in A: p [(x,y)  A] =

Note A joint pmf must satisfy the following conditions.

Y X	0 1 2 3
0 1 2	0.840 0.030 0.020 0.010 0.060 0.010 0.008 0.002 0.010 0.005 0.004 0.001

1. 
   Find the probability that there will be no errors made by robots
   
2. 
   Find the probability that there will be exactly one error
   
3. 
   Find the probability that there will be no improperly tightened bolts