The probability distribution for the rate of return on aninvestment is Rate of R

Question

The probability distribution for the rate of return on aninvestment is

                                      Rate of Return

                                         (InPercent)         Probability

                                                9.5                      .1

                                                9.8                      .2

                                               10.0                      .3

                                               10.2                      .3

                                               10.6                      .1

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

           b.   What is the expected rate of return?

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

Explanation / Answer

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

P(X>=10%)=0.3+0.3+0.1=0.7

           b.   What is the expected rate of return?

E(X)=9.5*0.1+9.8*0.2+10*0.3+10.2*0.3+10.6*0.1=10.03

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

E(X^2)=9.5^2*0.1+9.8^2*0.2+10^2*0.3+10.2^2*0.3+10.6^2*0.1=100.681

Var(X)=E(X^2)- [E(X)]^2 = 100.681-10.03^2=0.0801

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