Answer:
a. E(x) = 5.2000%
b. Variance = 122.16
Standard Deviation = 11.05
Step-by-step explanation:
Given
Scenario Probability Rate of Return
1 0.20 −16 %
2 0.40 7 %
3 0.40 14 %
a.
Expected Rate of Return = E(x)
E(x) = (-16% * 0.20) + (0.40 *7%) + (0.40 * 14%)
E(x) = -3.2% + 2.8% + 5.6%
E(x) = 5.2%
E(x) = 5.2000%
b.
Variance also known as the average of the squared differences from the Mean.
To calculate variance, start by calculating the mean, or average, of your sample. Then, subtract the mean from each data point, and square the differences. Next, add up all of the squared differences
Variance =
V = σ²= (−16 − 5.2)² * 0.20 + (7 − 5.2)² * 0.40 + (14 − 5.2)² * 0.40
V = σ² =122.16
Standard Deviation = σ = √SD
σ = √122.16
σ = 11.05124427383631
σ = 11.05 --- Approximated
Let the two numbers be x and y.
The difference between the numbers is 4. Therefore
x - y = 4 (1)
The sum of one-half of each number is 18, therefore
x/2 + y/ 2 = 18
x + y = 36 (2)
Add equations (1) and (2).
(x - y) + (x + y) = 4 + 36
2x = 40
x = 20
From (2), obtain
y = 36 - x = 36 - 20 = 16.
Answer: The two numbers are 16 and 20.
I just write not possible
Answer:
y=salary=32.000
x=years
salary after 15 years y+1800x
32000+1800(15)
32000+27000=59000
Step-by-step explanation:
<h3>
Answer: B. Yes, d = 3</h3>
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Explanation:
d = common difference, which is what we add on each time to get the next term
In this case, d = 3 means we add 3 each time to generate each new term
- -11+3 = -8
- -8+3 = -5
- -5+3 = -2
- -2+3 = 1
This pattern continues on forever.
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Another way to see that d = 3 is to notice this is the difference between any two adjacent terms.
- d = term2 - term1 = -8 - (-11) = -8 + 11 = 3
- d = term3 - term2 = -5 - (-8) = -5 + 8 = 3
- d = term4 - term3 = -2 - (-5) = -2+5 = 3
- d = term5 - term4 = 1 - (-2) = 1 + 2 = 3
Each gap is 3 units wide, which helps us see we have an arithmetic sequence.
A sequence like {-11,-8,-5,-2,2} is not arithmetic because the gap between the terms of -11,-8,-5,-2 is 3, but the gap from -2 to 2 is not 3. So the gap must stay the same the entire time to get an arithmetic sequence.