So I tried solving the first one and apparently failed miserably, attempted both twice and got it wrong each time and I have one submission attempt left, so any help is definitely appreciated!
1. Hotels R Us has kept the following recordes concerning the number of guests in a room.
Number of Guests | Probability
1 | .35
2 | .4
3 | .1
4 | .15
The Expected number of guests in a room is ____.
The standard deviation of the number of guests in a room is ___.
(Note: keep two decimals. Please keep more decimals during the middle steps so the final answer can match up.)
2. You are considering two mutual funds for your investment. The possible returns for the funds are dependent on the state of the economy and are given in the accompanying table.
State of the Economy | Fund A | Fund B
Good | 20% | 40%
Fair | 10% | 20%
Poor | -10% | -40%
You believe that the likelihood is 20% that the economy will be good, 50% that it will be fair, and 30% that it will be poor.
Which fund will you pick if you are risk averse?
Again, thanks in advance!!
For the first question:
To find the expected number of guests in a room, you need to multiply each number of guests by its corresponding probability and then sum up the results.
1. Multiply each number of guests by its probability:
Expected number of guests = (1 * 0.35) + (2 * 0.4) + (3 * 0.1) + (4 * 0.15)
2. Calculate the sum:
Expected number of guests = (0.35) + (0.8) + (0.3) + (0.6) = 2.05
Therefore, the expected number of guests in a room is 2.05.
To find the standard deviation of the number of guests in a room, you need to calculate the variance first, and then take the square root of the variance.
1. Calculate the variance:
Variance = [(1 - 2.05)^2 * 0.35] + [(2 - 2.05)^2 * 0.4] + [(3 - 2.05)^2 * 0.1] + [(4 - 2.05)^2 * 0.15]
2. Calculate the sum of the variances:
Variance = (0.0025 * 0.35) + (0.0025 * 0.4) + (0.9475 * 0.1) + (3.4725 * 0.15)
= 0.00875 + 0.01 + 0.09475 + 0.520875
= 0.634375
3. Calculate the standard deviation:
Standard deviation = square root of the variance = sqrt(0.634375) ≈ 0.796
Therefore, the standard deviation of the number of guests in a room is approximately 0.796.
For the second question:
To determine which fund to pick if you are risk-averse, you need to assess the potential returns and their likelihoods for each fund.
1. Calculate the expected return for each fund:
Expected return for Fund A = (0.2 * 0.2) + (0.1 * 0.5) + (-0.1 * 0.3) = 0.04 + 0.05 - 0.03 = 0.06 (or 6%)
Expected return for Fund B = (0.4 * 0.2) + (0.2 * 0.5) + (-0.4 * 0.3) = 0.08 + 0.1 - 0.12 = 0.06 (or 6%)
Both funds have an expected return of 6%.
2. Analyze the risk:
Fund A has a range of returns from -10% to 20%.
Fund B has a range of returns from -40% to 40%.
Since you are risk-averse, you would prefer the fund with the least amount of risk. Hence, Fund A is the better choice as it has a narrower range of returns.
Therefore, if you are risk-averse, you should pick Fund A.
I hope this explanation helps! Let me know if you have any further questions.