The standard deviation of the return on the investment in which the probability of doubling the investment is 0.72 and the probability that the investment will be halved is 0.28 will be 0.6734.
Given that the probability of doubling the investment is 0.72 and the probability that the investment will be halved is 0.28.
We are required to find the standard deviation of the rate of return on the investment.
Standard deviation can be find out by finding the square root of variance.
Suppose the investment is $1.
Probability Value
0.72 2
0.28 0.5
Expected value=Probability*Value
Expected value=0.72*2+0.28*0.5
=1.44+0.14
=1.58
Variance=E([tex]x^{2}[/tex])-[tex](Ex)^{2}[/tex]
=(0.72*4+0.28*0.25)-[tex](1.58)^{2}[/tex]
=(2.88+0.07)-2.4964
=2.95-2.4964
=0.4536
Standard deviation=[tex]\sqrt{variance}[/tex]
=[tex]\sqrt{0.4536}[/tex]
=0.6734
Hence the standard deviation of the rate of return on the investment is 0.6734.
Learn more about standard deviation at https://brainly.com/question/475676
#SPJ4
