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!!
Exp = 1(.35) + 2(.4) + 3(.1) + 4(.15)
= .35 + .8 + .3 + .6
= 2.05
Variance = 1^2 (.35) + 2^2(.4) + 3^2(.1) + 4^2(.15)
= .35 + 1.6 + .9 + 2.4
= 5.25
Sd = sqrt(5.25-(2.05)^2)
= 1.02
Thank you!!
And I also figured out the second one. APpreciate it!
If you're risk adverse you will go with Fund A because it has lower risk than Fund B.
To solve the first problem, you need to find the expected number of guests in a room and the standard deviation of the number of guests.
1. Expected number of guests in a room:
To find the expected value, you multiply each number of guests by its corresponding probability and then sum the results.
Expected value = (1 * 0.35) + (2 * 0.4) + (3 * 0.1) + (4 * 0.15)
Expected value = 0.35 + 0.8 + 0.3 + 0.6
Expected value = 2.05
Therefore, the expected number of guests in a room is 2.05.
2. Standard deviation of the number of guests in a room:
To find the standard deviation, you will need to calculate the variance first. The variance is the average of the squared deviations from the mean.
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)]
Variance = [(1.1025 * 0.35) + (0.0025 * 0.4) + (0.8925 * 0.1) + (3.1625 * 0.15)]
Variance = [0.385875 + 0.001 + 0.08925 + 0.474375]
Variance = 0.9505
To calculate the standard deviation, take the square root of the variance.
Standard deviation = √(0.9505)
Standard deviation = 0.9758 (rounded to four decimal places)
Therefore, the standard deviation of the number of guests in a room is 0.9758.
Now moving on to the second problem:
To determine which fund to pick if you are risk averse, you need to compare the expected returns of Fund A and Fund B based on the given probabilities.
1. Expected returns of Fund A:
Expected return for Fund A = (0.2 * 0.20) + (0.5 * 0.10) + (0.3 * (-0.10))
Expected return for Fund A = 0.04 + 0.05 - 0.03
Expected return for Fund A = 0.06
2. Expected returns of Fund B:
Expected return for Fund B = (0.2 * 0.40) + (0.5 * 0.20) + (0.3 * (-0.40))
Expected return for Fund B = 0.08 + 0.10 - 0.12
Expected return for Fund B = 0.06
Both Fund A and Fund B have the same expected return of 0.06.
If you are risk averse, you would prefer the fund with the least risk. In this case, Fund A has a lower potential loss compared to Fund B. Therefore, you should pick Fund A.
I hope this helps!