A random variable Y has the density Function
f(y) = { ey, y<0, 0, otherwise
a. Find E(e3Y/2)
b. Find the moment generating function for Y.
c. Find V(Y)
Answers
A random variable Y has the density Function f(y) = { ey, y<0, 0, otherwise
a.\(E(e^(3Y/2)) = [1/5] - [3e^(5/2)/10]\)
b.\(M(t) = 1/[(1-t)(t+1)]\)
c.\(V(Y) = ∫(y^2 + 2y + 1)eydy\) \(= [y^2e^y]/2 - ∫ye^ydy + [ye^y]/2 - ∫e^y\)
a. To find \(E(e^(3Y/2))\), we use the definition of expected value, which is the integral of the product of the random variable and its probability density function. We have: \(E(e^(3Y/2))\) \(= ∫e^(3y/2)f(y)dy\) \(= ∫e^(3y/2)eydy\), y<0 .Using integration by parts, we let \(u = e^(3y/2)\) and \(dv = e^y dy\). Then, \(du/dy = (3/2)e^(3y/2)\)and \(v = e^y\).
\(E(e^(3Y/2))\) \(= ∫e^(3y/2)eydy\) \(= [e^(3y/2)e^y/2] - ∫(3/2)e^(3y/2)e^y/2dy\)
\(= [e^(5y/2)]/5 - [3/5]∫e^(5y/2)dy\)
\(= [e^(5y/2)]/5 - [3e^(5y/2)/10] + C\)
Since f(y) = 0 for y ≥ 0, we know that \(E(e^(3Y/2))\) only depends on the integral of \(e^(3y/2)\)for y < 0. Evaluating the above expression at y = 0, we get:
\(E(e^(3Y/2)) = [1/5] - [3e^(5/2)/10]\)
b. To find the moment generating function (MGF) for Y, we use the definition of the MGF, which is the expected value of \(e^(tY)\) for all t in a neighborhood of 0. We have:
\(M(t) = E(e^(tY))\) \(= ∫e^(ty)f(y)dy\)\(= ∫e^(ty)eydy\) , y<0
Using integration by parts as before, we get:
\(M(t) = ∫e^(ty)eydy\) \(= [e^(ty)e^y]/(t+1) - ∫(t+1)(e^(ty)e^y)/(t+1)dy\)
\(= [e^(ty+2y)]/(t+1) - (t+1)M(t)\)
Simplifying, we get:
M(t)(t+1) = 1/(1-t)
M(t) = 1/[(1-t)(t+1)]
c. To find V(Y), we first need to find the mean or expected value of Y. Using the definition of expected value, we have:
E(Y) = ∫yf(y)dy = ∫yeydy, y<0. Using integration by parts once more, we get: E(Y) = ∫yeydy \(= [ye^y] - ∫e^ydy\) = -1 . The mean of Y is -1.
We use the definition of variance, which is the expected value of the squared difference between the random variable and its mean. We have:
\(V(Y) = E[(Y - E(Y))^2]\)\(= ∫(y + 1)^2f(y)dy\) \(= ∫(y^2 + 2y + 1)eydy\), y<0
Using integration by parts for the third time, we get:
\(V(Y) = ∫(y^2 + 2y + 1)eydy\)\(= [y^2e^y]/2 - ∫ye^ydy + [ye^y]/2 - ∫e^y\)
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Related Questions
You want to make a rectangular banner that is 16 feet long. You have no more than 50 feet of trim for the banner. What are the possible widths of the banner?
Answers
Answer:
So, the possible width of the banner would be 9 feet or less, since we have assumed a maximum total trim of 50 feet. If the width exceeds 9 feet, the total trim required would exceed the available trim of 50 feet. Therefore, the possible widths of the banner are 9 feet or less.
Step-by-step explanation:
Given:
Length of the banner (L) = 16 feet
Total trim available (T) = 50 feet
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (Length + Width)
In this case, the perimeter of the banner would be equal to the total trim available, since the trim goes all the way around the banner.
So, we can set up the equation as follows:
2 * (L + w) = T
Plugging in the given values:
2 * (16 + w) = 50
Simplifying the equation:
32 + 2w = 50
2w = 50 - 32
2w = 18
w = 18 / 2
w = 9
Compare 3/8 and 2/6
Pls help
If you do tyyy
Answers
Answer: 3/8 >2/6
Step-by-step explanation:
Aman is graduating from college and looking forward to his new role in his job as a computer scientist for a large firm. This is an example of
Answers
The answer is B. anticipatory socialization. Aman's anticipation and excitement about his new role as a computer scientist indicate his engagement in anticipatory socialization.
Anticipatory socialization refers to the process through which individuals learn and internalize the values, norms, and behaviors associated with a future role or status they aspire to have. In this case, Aman's graduation from college and his upcoming job as a computer scientist represent a transition to a new role.
As he looks forward to this new position, he is likely engaging in activities such as researching the company, learning about the responsibilities of a computer scientist, and acquiring the necessary skills to excel in his job. By doing so, Aman is preparing himself and adjusting his attitudes and behaviors to fit the expectations of his future role, which characterizes anticipatory socialization.
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The complete question is:
Aman is graduating from college and looking forward to his new role in his job as a computer scientist for a large firm. This is an example of
A.the imagination stage
B.anticipatory socialization.
C.the game stage.
D.looking-glass self
If f(x)=8^x and g(x) =9 , what is (f divided g ) (x)
A.8^x-9
B.8^x/9
C.(8/9)^x
D.9(8^x)
Answers
Answer:
f(x) / g(x) = 8^x / 9 --> B
Step-by-step explanation:
You just need to plug in the values
Answer:
B. 8^2/-9
Step-by-step explanation:
I think the first guy is right
Which type of angle is ZABC?
A
259
65°
B
O ZABC is a straight angle.
ZABC is a vertical angle.
O ZABC is a right angle.
O ZABC is a complementary angle.
Answers
Answer: right angle
Step-by-step explanation:
Looks like a right angle, where line AB and line BC meet is a 90 degree angle, making it a right angle.
The type of angle that is angle ABC is right angle because it is a 90 degrees angle.
What is a right angle ?A right angle is an angle that is 90 degrees.
In other word, any angle that is 90 degrees is a right angle.
Therefore, let's find angle ABC.
∠ABC = 25° + 65°
∠ABC = 90°
Therefore, ∠ABC is a right angle.
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Solve for x
X over 4 minus negative nine equals ten point one
X/4 - -9 = 10.1
Answers
Answer:
x=4.4
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
14x+9=10.1
Step 2: Subtract 9 from both sides.
14x+9−9=10.1−9
14x=1.1
Step 3: Multiply both sides by 4.
4*(14x)=(4)*(1.1)
x=4.4
Solve for x. {x}{3}+2=-13
Answers
3
x
+
2
=
−
13
Step 2: Subtract 2 from both sides.
3
x
+
2
−
2
=
−
13
−
2
3
x
=
−
15
Step 3: Divide both sides by 3.
3
x
3
=
−
15
3
x
=
−
5
Leonora is incubating eggs. For the eggs to hatch, the temperature in the incubator (1) needs to be at least 83°F. Which statement
represents the temperature it must be in the incubator for the eggs to hatch, in °F?
OA. 1283
OB. t>83
OC. t≤83
OD. t=83
Please help
I have to get this done by Friday
Answers
The statement represents the temperature it must be in the incubator for the eggs to hatch, in °F is t>83.
What is temperature ?
Temperature is a physical volume that expresses quantitatively the comprehensions of voguishness and dispassionateness. Temperature is measured with a thermometer. Thermometers are calibrated in colorful temperature scales that historically have reckoned on colorful reference points and thermometric substances for description.
What is Inequality ?
In mathematics, a relationship between two expressions or values that aren't equal to each other is called' inequality.' So, a lack of balance results in inequality.
The expression will be t 83° if variable T is used to denote the temperature. Considering that the temperature may be higher than or equal to 83°.
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What is the additive inverse of 3/4
Answers
From the given fraction , the additive inverse of \(\frac{3}{4} is -\frac{3}{4}\)
Given :
Additive inverse of 3/4
For any number , additive inverse of 'a' is -a
Additive inverse of a number is a number that is added with original number to get 0
For example , the additive inverse of 5 is -5 because 5+(-5) =0
To get additive inverse we multiply the given number by -1
So the additive inverse of \(\frac{3}{4} is -\frac{3}{4}\)
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ASAP!!!!!!!!! PLEASE help me with this question! This is really urgent! No nonsense answers please.
Answers
Answer:
\(\huge\boxed{Option \ C}\)
Step-by-step explanation:
∠CAD is the central angle and ∠CBD is the inscribed/circumference angle which means that
∠CAD = 2(∠CBD)
So, If ∠CBD = 55° then ∠CAD = 110°
hi guys
i need help only 19
Answers
slope: (y2-y1)/(x2-x1) = (5-3)/(2- -1) = 2/3
point intercept form: (y-y1) = m (x-x1)
(y-3) = 2/3 (x+1)
solve for y
y-3 = 2/3x + 2/3
y = 2/3x + 11/3
Find thw product of (x+3)(x-3)(x+7)
Answers
Answer:
x^3+7x^2−9x−63
Step-by-step explanation:
can i please have brainliest
find derivative of ² (20) = √₂2²² f 2-2 √1 t4 dt as your answer please input f' (2) in decimal form with three significant digits after the decimal place.
Answers
The value of f'(2) in decimal form with three significant digits after the decimal place is -1.14.
To find the derivative of the given function, we need to use the chain rule and the power rule of differentiation. Firstly, we can simplify the given function as:
²(20) = 2²² = 4¹¹
√₁ t⁴ = t²
Therefore, the given function can be written as:
f(t) = 4¹¹ × (t²)⁻²√₁
Now, using the power rule and the chain rule, we get:
f'(t) = -8 × t × (t²)⁻³√₁
f'(2) = -8 × 2 × (2²)⁻³√₁
f'(2) = -1.14 (rounded to three significant digits after the decimal place)
Therefore, the value of f'(2) in decimal form with three significant digits after the decimal place is -1.14.
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You earn $100 per month and want to save 10% in a savings account. Use the savings
calculator to find out how much your total savings would be in 5 years if your account
has an annual interest rate of 1%. (Do not include the $ sign in your reponse) PLEASE HELPP
Answers
With the annual interest of 1%, the total saving after 5 years is $6060.
Interest:
Interest is the amount for a particular principal amount of money at some rate of interest.
Given,
You earn $100 per month and want to save 10% in a savings account.
Here we have to use the savings calculator to find out how much your total savings would be in 5 years if your account has an annual interest rate of 1%.
Through the given details we have identified that,
Monthly earning = $100
Saving per month = 10%
So, in amount it can be
=> 100 x 10/100 = $10
So, for one year the saving without interest is
=> 10 x 12 = 1200
So, When we add the interest of 1% for the year,
Then the interest amount for one year will be,
=> 1200 x 1/100 = 12
So, the total amount including interest for one year,
=> 1200 + 12 = 1212
So, the savings after 5 years will be,
=> 5 x 1212
=> 6060.
Therefore, the total saving amount after 5 years is $6060.
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This is easy I just need the answer thanks!!! :)
Answers
Answer:
225 inches
Step-by-step explanation:
15 x 15 = 225
What is 6÷-1/2 please answer
Answers
Answer:
The correct answer is -12
Step-by-step explanation:
Hope I helped you!!
Find the area of this figure
Show work, please
Answers
Answer:
80 in2
Step-by-step explanation:
Here is my work shown in screeny
solve for m
-3/7m=12
A: M= -28
B: M= -26
C: M= 26
D: M= 28
Answers
Answer:
A
Step-by-step explanation:
Answer:
-3/7m=12
-3m/7=12 multiplying by 12 on both sides
-3m=12x7
-3m=84
divide by -3
-3m/-3= 84/-3
m= -28
Ans is A
49
11. What is the value of the expression m^3, when m=-8. (Hint: m to the the
third power)
Your answer
Answers
Hey there!
m^3
= -8^3
= -8 * -8 * -8
= 64 * -8
= -512
Therefore, your answer is: -512
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
DUE TODAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!!
Answers
Answer:
\(r = \sqrt{ {(6 - 2)}^{2} + {(1 - ( - 3))}^{2} } \)
\(r = \sqrt{ {4}^{2} + {4}^{2} } = \sqrt{16 + 16} = \sqrt{32} \)
So the equation of the circle is
\( {(x - 2)}^{2} + {(y + 3)}^{2} = 32\)
helpppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answers
Answer: c
Step-by-step explanation:
and then when you add all of the given measurements you will have the distance from clear lake to the end of her hike
Turner is reading his summer novel. He has timed himself and finds that he reads 4 pages every 5 minutes. What is his rate of reading per minute?
Answers
Answer:
0.8
Step-by-step explanation:
1 minute = 0.8 pages read 0.8 x 5 minutes = 4 pages read
What is the slope of the line that passes through the points (-9, 5)and (-17, 5) ? Write your answer in simplest form.
Answers
Answer:
0
Step-by-step explanation:
\(\frac{y2-y1}{x2-x1}\)
\(\frac{5-5}{-17-(-9)}=\frac{0}{-8} =0\)
slope=0
Find the Amount (A) (Principal Rs 50000 Time = 7 years interest = 3%.
Answers
Answer: Rs 60500
Step-by-step explanation:
Principal = Rs 50000 = p
Time = 7 years = t
Simple interest rate = 3% = r
Interest = p*t*r/100
using above formula,
50000*7*3/100=10500
So, final amount = principal + interest = 50000+10500 = Rs 60500
Triangle PQR has its vertices at the following coordinates:
P(5,-4) Q(3,-5) R(1,-1)
Give the coordinates of the image triangle P'Q'R' after a 90° counterclockwise
rotation about the origin.
Answers
Answer:
P'(4, 5) Q'(5, 3) R'(1, 1)
Step-by-step explanation:
When rotating a point 90 degrees counterclockwise about the origin our point T(x,y) becomes T'(-y,x).
In the first year of production
a play sells 1572 tickets, in its
second year it sells 1753
tickets, in its third year it sells
152 less than in its second
year. How many tickets are
sold in 3 years?
Please add the working out too
Answers
Matt bowled three strings. His scores were 220, 166, and 181. What was his average for the three strings?
Answers
Answer:
189
Step-by-step explanation:
To find his average, we will find the mean. This means we will add 220+166+181 to get 567. When finding the mean we divide the answer but the total amount of addends. In our case we have 3 so we divide 567 by 3.
567 divided by 3 = 189
I hope this helps :DDDDDDDDDDD
According to the table above, what percent of patients with type-B blood are 50 years old or younger?
Answers
The percentage of patients with type-B blood that are 50 years old or younger is calculated as follows:
P = number of patients with type B blood that are 50 years or younger / number of patients with type B blood x 100%
How to calculate a percentage?Two parameters are used to calculate a percentage, as follows:
Number of desired outcomes a.Number of total outcomes b.The proportion is given by the number of desired outcomes divided by the number of total outcomes, while the percentage is the proportion multiplied by 100%.
Hence the rule is given as follows:
P = a/b x 100%.
Missing InformationThe problem is incomplete and the table could not be found on the internet, hence the general procedure to obtain the percentage is presented.
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The difference of two numbers is 5, and their sum is 17. What are the two numbers?
Answers
Answer:
11 and 6
Step-by-step explanation:
11-6=5 <--- difference
11+6=17 <--- sum
On average, 24% of customers who buy shoes in a particular store buy two or
more pairs. One weekend, 350 customers purchased shoes. How many can be
predicted to buy two or more pairs? If 107 customers buy more than two pairs,
did more customers than normal buy two or more pairs?
Answers
Answer:
84 Customers
Step-by-step explanation:
To predict how many customers out of the 350 will buy two or more pairs, you need to find 24% of the 350 customers: 24% * 350 = 84 Customers.