A fisherman is restricted to catching at most two red groupe

A fisherman is restricted to catching at most two red grouper per day when fishing in the Gulf of Mexico. A field agent for the wildlife commission often inspects the day\'s catch for boats as they come to shore near his base. He has found that the number of red grouper caught has the following distribution. Assuming that these records are representative of red grouper daily catches in the Gulf, find the expected value, the variance, and the standard deviation for the individual daily catch of red grouper.

Solution

The expectation is: 0*0.2+1*0.7+2*0.1=0.9

The variance is:

0*0*0.2+1*1*0.7+2*2*0.1-0.9^2

=0.29

The standard deviation is root over 0.29=0.53