The probability distribution for the rate of return on an investment is Rate of

Question

The probability distribution for the rate of return on an investment is

                                       Rate of Return

                                          (In Percent)          Probability

                                                9.5                       .1

                                                9.8                       .2

                                                10.0                       .3

                                                10.2                       .3

                       10.6          

a.   What is the probability that the rate of return will be at least 10%?

              b.   What is the expected rate of return?

                        c.   What is the variance of the rate of return?

Explanation / Answer

P( return = 10.6) = 1 - 0.1 -0.2 -0.3 - 0.3 = 0.1

a)

P(the rate of return will be at least 10%) = P(return = 10.0) + P(return=10.2) +P(return= 0.6)= 0.3 + 0.3+0.1 = 0.7

b)

Expected return = 9.5*0.1 + 9.8*0.2 + 10.0*0.3 + 10.2*0.3 + 10.6*0.1 = 10.03

c)

Variance = ((9.5-10.03)^2)*0.1 + ((9.8-10.03)^2)*0.2 + ((10.0-10.03)^2)*0.3 + ((10.2-10.03)^2)*0.3 + ((10.6-10.03)^2)*0.1 = 0.0801

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