Homework SourseProbability and statistics A small convenience store has two
Probability and statistics
A small convenience store has two checkout stations. Suppose that the joint probability mass function of the random variables X=number of customers at station 1 and Y=number of customers at station 2 is as tabulated next. Compute the covariance and correlation between X and Y
| Y | ||||
|---|---|---|---|---|
| No.Columns | 0 | 1 | 2 | |
| 0 | 0.3 | 0.08 | 0.02 | |
| X | 1 | 0.08 | 0.2 | 0.05 |
| 2 | 0.02 | 0.05 | 0.2 |
Solution
Cov(X,Y)=E(XY)XY
For any random variables X and Y (discrete or continuous!) with means X and Y
X = (0*0.4+1*0.23+2*2.7)/3=1.87
Y = (0*1.3+1*3.3+2*2.7)/3= 2.9
Cov(X,Y)=E(XY)XY
E(XY)= xyf(xy)
= 0 + 0.8+0.02+0.08+0.2+0.10+0.04+0.05+0.8=2.09
Cov(X,Y) = 2.09-5.42=-3.9
