A bakerman sells 5 types of cakes. Profits due to the sale of each type of cake is respectively Rs. 3, Rs. 2.5, Rs. 2, Rs. 1.5, Rs. 1. The demands for these cakes are 10%, 5%, 25%, 45% and 15% respectively. What is the expected profit per cake?

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#### Solution

Let X = demand for each type of cake (according to the profit)

P(X = 3) = 10% = 10/100 = 0.1

P(X = 2.5) = 5% = 5/100= 0.05

P(X = 2) = 20% = 20/100= 0.2

P(X = 1.5) = 50% = 50/100= 0.5

P(X = 1) = 15% = 15/100 = 0.15

∴ The probability distribution table is as follows:

X | 3 | 2.5 | 2 | 1.5 | 1 |

P(X) | 0.1 | 0.05 | 0.2 | 0.5 | 0.15 |

E(X) = ∑x_{i} ⋅P(x_{i})

= 3(0.1) + 2.5(0.05) + 2(0.2) + 1.5(0.5) + 1(0.15)

= 0.3 + 0.125 + 0.4 + 0.75 + 0.15 = 1.725

= 1.73

∴ Expected profit per cake = Rs. 1.73

Concept: Statistics - Bivariate Frequency Distribution

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