Question

Your friend is asking you to invest in his bakery, and you have 35000. The returns are volatile, and you may get either 43000 with a probability of 0.44 or 27000 with a probability of 0.56.



a. What is the expected value of the investment?



b. Will you buy the refrigerator? Why?



c. Identify the mean, variance, and standard deviation.

Answer 1

Solution:

a.

The expected value of the investment$=43000 \times 0.44 + 27000 \times 0.56$

$=18920+15120 \\=34040$

b. I have 35000. I may get an expected value of 34040, which is less than the amount I have to invest. I will not buy the refrigerator as it provides me the loss.

c.

Mean$=E[X]=34040$

$E[X^2]=43000^2\times0.44+27000^2\times0.56=1221800000$

Now, variance$=\sigma^2=E[X^2]-(E[X])^2$

$=1221800000-34040^2 \\=63078400$

Standard deviation$=\sigma=7942.191$