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.

Number of Grouper 0 1 2

Probability 0.2 0.7 0.1

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

Consider the table:

Thus,

Thus,      
      
E(x) = Expected value = 0.9  
Var(x) = E(x^2) - E(x)^2 =    0.29  
s(x) = standard deviation = 0.538516481 [ANSWERS]