Answer to Question #245359 in Statistics and Probability for Pogo

Question

2. 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$=\sigma=7942.191$