Answer:
a) E(x)=2.5 V(x)=1.59
b) E(R)=17 V(R)=6.36
c) The probability that, when the four make their orders, everyone gets what they ordered is P=0.66.
Step-by-step explanation:
a) The mean E(x) can be calculated as:
The variance V(x) can be calculated as:
b) The revenue can be expressed as:
Then, the expected value of R canbe expressed in function of x:
The expected revenue is $17.
The variance of R is
c) In the case there are only 3 Cokes and 3 Sprites available, the only orders that can not be fullfilled are when X=0 (they order 4 Sprites) and X=4 (they order 4 Cokes).
The probability of these events is:
So, the probability of everyoned getting what they ordered is:
The probability that, when the four make their orders, everyone gets what they ordered is P=0.66.