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A project has a 60% chance of doubling your investment in 1 year and a 40% chance of losing half your money. What is the standard deviation of this investment?

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thuyntd

Answer:

The standard deviation is 0.73 times the value of your investment

Explanation:

Standard deviation is the measure of dispersion from the mean of the group as a whole.

It is a group statistic, so it is necessary to see the project's result as a group result.

Let P be the value of your investment.

If you can invest 100 times in the project then after 1 year you will receive 2P for 60 times and 0.5P for 40 times. The 40% ad 60% information is not conditioned on a sample so the case should be considered a measurement on population.

Mean = [tex]\frac{\sum x_{i}}{n}[/tex] = [tex]\frac{60 \times 2P + 40 \times 0.5P}{100}[/tex]

Variance = [tex]\frac{\sum {(x_{i} - Mean)^{2}}}{n}[/tex]

= [tex]\frac{(2P - 1.4P)^2 \times 60 + (0.5P - 1.4P)^2 \times 40} {100} =0.54P^{2}[/tex]

Standard Deviation = [tex]\sqrt{Variance}[/tex] = [tex]\sqrt{0.54P^{2}}[/tex] = 0.73P

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