Answer:
[tex]E(x) = 10.8\% \\\\[/tex]
The fruit company’s expected returns are 10.8%
Step-by-step explanation:
The expected returns of the fruit company is given by
[tex]E(x) =\sum (x \cdot P(x)) \\\\[/tex]
For the given case,
Returns in normal rainfall = x₁ = 20% = 0.20
Returns in drought = x₂ = -3% = -0.03
Probability of normal rainfall = P(x₁) = 60% = 0.60
Probability of drought = P(x₂) = 40% = 0.40
So, the expected value of returns is
[tex]E(x) = x_1 \cdot P(x_1) + x_2 \cdot P(x_2) \\\\E(x) = 0.20 \cdot 0.60 - 0.03 \cdot 0.40 \\\\E(x) = 0.12 - 0.012 \\\\E(x) = 0.108 \\\\E(x) = 10.8\% \\\\[/tex]
Therefore, the fruit company’s expected returns are 10.8%
