Answer to Question #270429 in Statistics and Probability for Light

Question

You are considering acquiring shares of common stock in ABC Corporation. Your rate of return expectations are as follows:

Possible rate of return - 0.10 0.00 0.10 0.25 Probability 0.20 0.25 0.35 0.20

(i) Compute the expected return on the investment (3 marks) (ii) Compute the standard deviation of the expected return. (3 marks)

(b) There are 15 police officers at a station. The officer – in charge has decided to send 8 officers on patrol, 4 of them to control road traffic and the rest to remain at

the office. In how many different ways can she assign the officer to the tasks?

Answer 1

(a) As i understand there is a mistake in the condition, there are two values 0.1 in the possible rate of return, which is impossible. I will put x instead of the second 0.1 value and then you can put your value instead of x to get the answer. So, lets represent data as a table

X - rate value, P - corresponding probability

(i) The common formula for expected value is $E(x)=\sum_{k=1}^{k=n}x_i*p_i$ , where n - total number of values

In the given case

$E(x)=0.1*0.2+0*0.25+x*0.35+0.25*0.2=0.07+0.35x$

(ii) $\sigma=\sqrt{D}$ , where $\sigma$ - standard deviation, D - variance

$D=E(x^2)-(E(x))^2$

$E(x^2)=0.1^2*0.2+0^2*0.25+x^2*0.35+0.25^2*0.2=0.0145+0.35x^2$

$D=0.0145+0.35x^2-(0.07+0.35x^2)=0.0145+0.35x^2-0.0049-0.049x-0.1225x^2=0.2275x^2-0.049x+0.0096$

$\sigma=\sqrt{0.2275x^2-0.049x+0.0096}$

(b) Since the order of choosing policemans is not important, then total value n will be

$n={15 \choose 4}*{11 \choose 4}=1365*330=450450$