Originally Posted by
somestudent2 A heavy equipment sales person can contact either one or two customers per day with probability 1/3 and 2/3 respectively. Each contact will result in no sale or a $50 000 sale with the probabilities .9 and .1. Give the probability distribution for daily sales. Find the mean and standard deviation of the daily sales.
Here is how I started:
Let Y denote # of daily sales. Then Range of Y = {0,1,2}
Given: P(contacting 1) = 1/3
P(contacting 2) = 2/3
P(Sale) = 1/10
P(No Sale) = 9/10
Possible outcomes:
Contacted 1 sold 0
Contacted 1 sold 1
Contacted 2 sold 0
Contacted 2 sold 1
Contacted 2 sold 2
Now I have a problem in going further, how do I calculate these probabilities to create distribution of Y. For example how to calculate contacted 2 sold 1 or contacted 2 sold 2? Are the events independent?
Should it be something like this
P of SS(Sale Sale) 1/10 * 1/10 = 1/100
P of SN(Sale no Sale) 1/10*9/10= 9/100
P of NN(no sale no sale) 9/10 *9/10 = 81/100
then use these values to calculate:
P(Y= 0)= 1/3 * 81/100 + 2/3 * 81/100 = 81/100
P(Y = 1) = 1/3 * 9/100 + 2/3 * 9/100 = 9/100
P(Y = 2) = 2/3 * 1/100 + 1/3 * 1/100 = 1/100
?