SOLUTION: a. The following table gives the joint probability distribution of the random variables X and Y , where X is the first - year rate of return expected from investment A while Y

Question 1198127: a. The following table gives the joint probability distribution of the random
variables X and Y , where X is the first - year rate of return expected
from investment A while Y is the first - year rate of return expected from
investment B.
Table 5: Rates of Return on Two Investments
Y(%) X(%)
-10 0 20 30
20 0.27 0.08 0.16 0
50 0 0.04 0.1 0.35
i. Calculate the expected rate of return from investment B.
ii. Find the conditional expectation of Y , given X = 20.

Answer by onyulee(41) (Show Source): You can put this solution on YOUR website!
**i. Calculate the expected rate of return from investment B**
* To calculate the expected rate of return from investment B, we'll sum the products of each possible return of B (Y) and its corresponding probability.
* **Expected Return of B (E[Y]) =**
* (20% * 0.27) + (20% * 0.08) + (20% * 0.16) + (50% * 0) + (50% * 0.04) + (50% * 0.1) + (50% * 0.35)
* = 5.4 + 1.6 + 3.2 + 0 + 2 + 17.5
* = **34.7%**
**ii. Find the conditional expectation of Y, given X = 20**
* We need to find the expected return of investment B (Y) when investment A (X) has a return of 20%.
* **Conditional Probability Table (X = 20):**
| Y(%) | Probability (given X = 20) |
|---|---|
| 20 | 0.16 / (0.16 + 0.1) = 0.6154 |
| 50 | 0.1 / (0.16 + 0.1) = 0.3846 |
* **Conditional Expectation of Y given X = 20 (E[Y|X=20]) =**
* (20% * 0.6154) + (50% * 0.3846)
* = 12.308 + 19.231
* = **31.539%**
**In summary:**
* The expected rate of return from investment B is **34.7%**.
* The conditional expectation of Y (the return on investment B) given that X (the return on investment A) is 20% is **31.539%**.

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