1. A company has a cash portfolio measured in millions. The drift is 0.1 per month, variance is 0.16per month. The initial cash is 2.0. a) Find the probability distribution after 6 months and after 1 year. b) Find the probability of a negative cash position at the end of 6 months and the end of 1 year. c) At what time in the future is the probability of a negative distribution greatest.
Answer:
Step-by-step explanation:
From the information given:
The probability distribution at the end of 6 months is determined as follows:
After 6 months;
Mean of probability distribution = value of Initial cash + [tex]\alpha[/tex]T
=2.0 +(0.1 × 6)
=2.6
After 6 months;
The probability distribution's standard deviation is estimated by using the following formula:
Standard deviation:
[tex]= b\sqrt{T}[/tex]
[tex]= 0.4 \times \sqrt{6}[/tex]
= 0.9798
Hence, after 6 months;
The company's cash position is supposed to be allocated monthly, with the following expenses.
Mean 2.6
Standard deviation 0.9798
Variance 0.96
After 12 months, the probability distribution is as follows:
Mean = value of Initial cash + [tex]\alpha[/tex]T
= 2.0 +(0.1 × 12)
= 3.2
The standard deviation is:
The standard deviation of probability distribution = [tex]b \sqrt{T}[/tex]
[tex]= 0.4 \times \sqrt{12}[/tex]
= 1.3856
Hence, after 6 months;
The company's cash position is supposed to be allocated monthly, with the following expenses.
Mean 3.2
Sandard deviation 1.3856
Variance 1.92
b)
in 6-month distribution, the probability of the negative value of the cash position is as follows.
Now, for us to find the negative cash distribution;
We need to estimate the z -scores value.
The z-score inform us greatly on the concept of how far a particular data point is from the mean.
For a normal distribution;
[tex]z = \dfrac{x-\mu}{\sigma}[/tex]
Here;
the value of x = zero as a result that if it exceeds zero. the cash position will be negative.
∴
[tex]z = \dfrac{x-\mu}{\sigma}[/tex]
[tex]z = \dfrac{0 - 2.6}{0.9798}[/tex]
[tex]z = -2.6536[/tex]
Using the standard distribution tables, it is now possible to calculate that the likelihood N(-2.65) equals 0.004 or 0.4 percent.
As a result, there's a 0.4 percent chance of getting a negative cash balance after six months.
For 12 months distribution:
The Probability of negative cash position is calculated as follows:
[tex]z = \dfrac{x-\mu}{\sigma} \\ \\ z = \dfrac{0-3.2}{1.3856} \\ \\ z = -2.3094[/tex]
Using the standard distribution tables,
N(-2.31) equals 0.0104 or 1.04 percent.
As a result, there's a 1.04 percent chance of getting a negative cash balance after 1 year
c) To determine the time period over which the likelihood of achieving a negative cash condition is highest, it's necessary to examine the z-score more closely. Essentially, the z-score measures the difference between a given value(x) and the mean of all potential values [tex](\mu)[/tex], expressed in terms of the total set's standard deviation [tex](\sigma)[/tex]
This suggests that the higher the z-score, the greater the difference occurring between x and [tex]\mu[/tex], and thus the likelihood of receiving x is minimal. As a result, the best chance of finding a certain value is when the z-score is the lowest.
To do so, calculate the derivative of the z-score in relation to the time interval. The point where the derivative is equivalent to zero is where the z-scores are at their lowest.
The first step is to go over the z-score formula in more detail, as seen below.;
[tex]z = \dfrac{x-\mu}{\sigma} \\ \\ z = \dfrac{0-(initial \ value + \alpha T)}{b \sqrt{T}} \\ \\ z = \dfrac{-initial \ value }{b\sqrt{T}}-\dfrac{a \sqrt{T}}{b} \\ \\[/tex]
Now, compute the derivative of this equation with respect to T as follows:
[tex]\dfrac{dz}{dT}= \dfrac{initial \ value \times T^{-\dfrac{3}{2}}}{2b} - \dfrac{aT^{-\dfrac{1}{2}}}{2b}[/tex]
Now, figure out the value of T at which this derivative is equal to zero by substituting all values as follows:
[tex]0 = \dfrac{2.0 \times T^{-\dfrac{3}{2}}}{2\times 0.4}- \dfrac{0.1 \times T^{-\dfrac{1}{2}}}{2 \times 0.4} \\ \\ \\ 0.1 \times T^{-\dfrac{1}{2}}= 2.0 \times T^{-\dfrac{3}{2}} \\ \\ \\T = \dfrac{2}{0.1} \\ \\ \\ T = 20[/tex]
As a result, the time period in which achieving a negative cash condition is = 20 months.
PLS ANSWER ASAP! Only answer if you are sure that it is correct & no links or i will report you
Given f(x) = -x^2 - 2x + 4, find each of the following,
Symmetric point:
Minimum of f:
Maximum of f:
Is f a one-to-one
Does f have an inverse?
Increasing on
Decreasing on
Answer:
Symmetric point: x = -1; (-1, 5)
Minimum of f: None; approaches -∞.
Maximum of f: y = 5.
Is f(x) a one-to-one: No, it fails the horizontal line test and is not injective.
Increasing from: -∞ to -1; (-∞, -1)
Decreasing from: -1 to ∞. (-1, ∞)
Answer:
Given f(x) = -x^2 - 2x + 4, find each of the following,
Step-by-step explanation:
f(x) = -x²-2x+4
f(2) = (-2)²-2×2+4
f(2) = 4-4+4
f(2) = 4
a) Work out 4 1/7+1 1/2
Answer:
5 9/14
Step-by-step explanation:
easy maffs
Acellus
Find the measure of < 4.
44
158°
{
*4 = [?]
Fnter
<4=22°
Answer:
<4+158=180 co interior angle
<4=180-158=22°
Answer:
solution given:
<4+<158°=180°[co- interior angle]
<4=180°-<158°=22°
<4=22° is your answer
3. The cone below is intersected by a
horizontal plane. What is the shape of the
cross section?
Answer:
It depends were you are looking from but there is shows D. Oval so ig thats
the answer
Employee Earnings per
month($)
1
1,200
2
2,600
3
1,800
4
1,450
5
3,500
6
2,800
7
12,500
8
3,200
Answer:
actually its depend on how is he working day by day
A recipe calls for ¾ cups of molasses. If you triple the recipe, how much molasses is needed?
A recipe calls for ¾ cups of molasses. If you triple the recipe, 9/4 cups of molasses would be needed
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A recipe calls for ¾ cups of molasses. If you triple the recipe, the molasses is:
Amount of molasses needed = 3 * (3/4) cup = 9/4 cups
A recipe calls for ¾ cups of molasses. If you triple the recipe, 9/4 cups of molasses would be needed
Find out more on equation at: https://brainly.com/question/2972832
The equation for the perimeter around Claire's garden is a:
Group of answer choices
Linear Function
Exponential Function
Quadratic Function
Absolute Value Function
Answer:
Linear Function
Step-by-step explanation:
I just took the test and got it right.
Kammys mom gave her $85 to go shopping if she spent $118 how much of her own money did curry use
When graphing a system of equations with infinitely many solutions, the slopes of the two lines will be ________.
hi does anyone have the answer for this? 100 points if answered :))
Answer:
15 feet
Step-by-step explanation:
This is already factored for the zeros of the quadratic. If x - 5 = 0 and x - 20 = 0 then x = 5 and 20. The ball was kicked 5 feet out and landed at 20 feet down the field. The difference is 15 feet. That's how far the ball traveled from its initial position on the ground to its landing place.
So 15 feet from where it was kicked.
PLEASE HELPS!!!!!!!!!!!!!!!!!!!!!!! I WILL GIVE BRAINLIEST AND EXTRA POINTS!!!!!!!!!!!!!!!!!!!!!
Answer:
Yes
Yes
No
No
Step-by-step explanation:
please answer i will give crown :D
Answer:
0.24
Step-by-step explanation:
1.679-1.439
What type of world would you want to escape to right now if you could ?
Wat is a mixed number or whole number: 11/3
Answer:
Not exactly sure what your asking but 11/3 as a mixed number is 3 2/3
Answer:
3 2/3 is the simplified version of 11/3
Step-by-step explanation:
I need help with solving this equation.
Answer:
66 m².
Step-by-step explanation:
From the question given above, the following data were obtained:
Diagonal 1 (d₁) = 11 m
Diagonal 2 (d₂) = 12 m
Area (A) =?
The area of a rhombus when the diagonals are given can be obtained as follow:
A = ½(d₁d₂)
A = ½ × (11 × 12)
A = ½ × 132
A = 66 m²
Thus, the area of the rhombus is 66 m²
Marie found that 4 bags of leaves weigh 6 pounds and 8 bags of leaves weigh 12 pounds. She made a graph to help her find the weight of other numbers of bags. On a coordinate plane, a line is drawn through points (4, 6) and (8, 12). Which ordered pair follows the pattern in the graph? (2, 4) (3, 4) (6, 8) (6, 9)
Answer:
D 6,9
Step-by-step explanation:
Please help answer !:)
Will give brainlst!!
Have a nice day
Answer:
10, exponents, 10, expression
Step-by-step explanation:
n exponential function and a quadratic function are graphed below. Which of the following is true of the growth rate of the functions over the interval
The exponential grows at half the rate of the quadratic.
The exponential grows at the same rate as the quadratic.
The exponential grows at twice the rate of the quadratic.
The exponential grows at four times the rate of the quadratic.
https://brainly.com/question/4184462
Answer:
the answer is B)
Step-by-step explanation:
edg2021 :>
Olaf wants to buy a guitar that costs $600. He makes $3 per day. How many days will it take Olaf to save enough money to buy the guitar
Answer:
200 days
Step-by-step explanation:
600/3 = 200
Answer:
200 days
Step-by-step explanation:
Simple: You divide the cost of the guitar by the amount he gets paid per day. Hope this helps :)
Write a jingle to advertise
favorite dessert to the tune of
"Twinkle, Twinkle Little Star."
What is so special about this
dessert? How can you describe it
in a memorable, catchy way?
Y’all someone help no link ,will be reported
My Jingle:
Ice cream cake - oh, ice cream cake...
How I love the way you taste...
You melt in my mouth with every bite...
Dreams of you keep me up at night...
Ice cream cake - oh, ice cream cake...
How I love the way you taste.
I hope you like it!
Each side length is doubled. What is the PERIMETER of the new figure?
Answer:
24 units
Step-by-step explanation:
Original perimeter:
5+4+3=12
When each side length is doubled, the original perimeter is doubled.
12*2=24
Answer:
if the length of each side is is doubled then
5×2 = 10
4×2 = 8
3×2 = 6
perimeter of new figure = 10 + 8 + 6
= 24 units
hope this helps good day mate
Ava swam for 154 minutes during her first week of vacation. In her two weeks of vacation, she swam for a total of 357 minutes. How many more minutes did she swim for in the second week than in the first week?
Answer:
Ava swam 203 more miles
Step-by-step explanation:
357-154=203
what is the measure of angle xyz?
Answer:
The answer is B. 93
Step-by-step explanation:
186/2 is 93
Answer:
welp now i can add my answer although the other dude got it before me so yea other person is right
Step-by-step explanation:
What are the ordered pairs of the solutions for the
following system of equations?
Answer:
(3,1);(6,-2)
Step-by-step explanation:
I pretty much just looked at where they both intersected with each other and you'll get your answer.
A farmer is worried that a recent salmonella outbreak may have come from the carrots on his farm. He wants to test the carrots at the farm, but it will ruin the crop if he tests all of them.
a. If the farm has 10,000 carrots growing, describe a method that would
produce a random sample of 10 plants.
b. Why would a random sample be useful in this situation?
Answer: for b. Step-by-step explanation: The random sample would show multiple outcomes of the carrot growth and the combinations, i believe
a farmers market sells apples for $2.30 per pound. what would be the cost of 3 2/5 pounds of apples
Answer:
7.20
Step-by-step explanation:
Answer:
7.20 or 6.90
Step-by-step explanation: most likely 7.20 because 3 pounds of apples is 6.90 so adding a half to that would be 7.20
The amount of time, in hours, that a computer functions before breakingdown is a continuous random variable with probability density functiongiven byfX(x) ={1100e−x/100x≥00x <0.What is the probability that1. a computer will function between 50 and 150 hours before breakingdown (3 pts)2. It will function less than 100 hours? (3 pts)3. It will function exactly 100 hours before breaking down? (3 pts)
Answer:
[tex]P(50 < x < 150) =0.3834[/tex]
[tex]P(x = 100) =0.0074[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \left \{ {{\frac{1}{100}e^{-x/100}\ x\ge 0} \atop {0\ x<0}} \right.[/tex]
Solving (a): Probability that it will function between 50 and 150 hr before it breaks down
This is represented as:
[tex]P(50 < x < 150) = \int\limits^{150}_{50} {f(x)} \, dx[/tex]
So, we have:
[tex]P(50 < x < 150) = \int\limits^{150}_{50} {\frac{1}{100}e^{-x/100}} \, dx[/tex]
Integrate:
[tex]P(50 < x < 150) =- e^{-x/100}|\limits^{150}_{50}[/tex]
This gives:
[tex]P(50 < x < 150) =- e^{-150/100} - - e^{-50/100}[/tex]
[tex]P(50 < x < 150) =- e^{-150/100} + e^{-50/100}[/tex]
[tex]P(50 < x < 150) =- e^{-1.5} + e^{-0.5}[/tex]
[tex]P(50 < x < 150) =- 0.2231 + 0.6065[/tex]
[tex]P(50 < x < 150) =0.3834[/tex]
Solving (a): Probability that it will function exactly 100 hr before it breaks down
This is represented as:
[tex]P(x= 100)[/tex]
This can be rewritten as:
[tex]P(x= 100) = P(99<x<101)[/tex]
So, we have:
[tex]P(99 < x < 101) = \int\limits^{101}_{99} {f(x)} \, dx[/tex]
So, we have:
[tex]P(99 < x < 101) = \int\limits^{101}_{99} {\frac{1}{100}e^{-x/100}} \, dx[/tex]
Integrate:
[tex]P(99 < x < 101) =- e^{-x/100}|\limits^{101}_{99}[/tex]
This gives:
[tex]P(99 < x < 101) =- e^{-101/100} - - e^{-99/100}[/tex]
[tex]P(99 < x < 101) =- e^{-101/100} + e^{-99/100}[/tex]
[tex]P(99 < x < 101) =- e^{-1.01} + e^{-0.99}[/tex]
[tex]P(99 < x < 101) =- 0.3642 + 0.3716[/tex]
[tex]P(99 < x < 101) =0.0074[/tex]
Hence:
[tex]P(x = 100) =P(99 < x < 101) =0.0074[/tex]
-4x + 3y = -2
Y = x - 1
Answer:
(-1, -2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsSolving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define
-4x + 3y = -2
y = x - 1
Step 2: Solve for x
Substitution
Substitute in y: -4x + 3(x - 1) = -2[Distributive Property] Distribute 3: -4x + 3x - 3 = -2Combine like terms: -x - 3 = -2[Addition Property of Equality] Add 3 on both sides: -x = 1[Division Property of Equality] Divide -1 on both sides: x = -1Step 3: Solve for y
Substitute in x [Original Equation]: y = -1 - 1Subtract: y = -2