The probability that an investment will double is 0.84, and the probability that it will be halved is 0.16, so the standard deviation of the return on investment will be 0.5499.
Given that there is a 0.84 percent chance that the investment will double and a 0.16 percent chance that it will be half.
We must determine the rate of return on investment's standard deviation.
By calculating the square root of the variance, one can determine the standard deviation.
Suppose the investment is $1.
Probability Value
0.84 2
0.16 0.5
Expected value = Probability * Value
Expected value (EV) = (0.84 × 2) + (0.16 × 0.5)
EV = 1.68 + 0.08
EV = 1.76
Variance = E(x²) - (Ex)²
V = [(0.84 × 2²) + (0.16 × (0.5)²)] - (1.76)²
V = [(0.84 × 4) + (0.16 × 0.25)] - 3.0976
V = [3.36 + 0.04] - 3.0976
V = 3.4 - 3.0976
V = 0.3024
Standard deviation = [tex]\sqrt{Variance}[/tex]
SD = [tex]\sqrt{0.3024}[/tex]
SD = 0.5499
Hence, the standard deviation of the rate of return on the investment is 0.5499.
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