A backerman sells 5 types of cakes .Profit due ot sale of each type of cake is respectively 3,2.5,2,1.5 and 1. The demands for these cakes are 10%,5%,20%,50 and 15% respectivley. What is the expected profit per cake ?

Explanation

Let X be the profit due to sale of the cake .
Then X take the value 3,2.5,1.5, 1
`therefore P(X = 3) = 10% =(10)/(100)`
` P(X = 2.5) = 5% = (5)/(100)`
`P(X=2) = 20% = (20)/(100)`
`P(X = 1.5) = 50% = (50)/(100)`
`P(X = 1) = 15% = (15)/(100)`
`therefore` the probability distribution of X is as follows

`therefore` expected profit per cake .
`= E (X) = sum X.P(X)`
` = 3((10)/(100)) +(2.5)((5)/(100))+2((20)/(100)) +(1.5)((50)/(1000)) +1((15)/(100))`
` = (30)/(100) = 1.725 = 1.73`