Given that $Y\sim\text{Exp}(A)$, the probability density function of $Y$ is $f_Y(y)=Ae^{-Ay}$ for $y\geq 0$.
Let $X\sim\text{Poisson}(Y)$. Then, the conditional probability
mass function of $X$ given $Y=y$ is
P(X=k∣Y=y)=e−yykk!,k=0,1,2,…
To find the mean and variance of $X$, we first find $E[XY]$ and $E[X^2Y]$.
\begin{align*}
E[XY] &= \int_{0}^{\infty} E[XY|Y=y]f_Y(y)dy \
&= \int_{0}^{\infty} E[Xy]Ae^{-Ay}dy \
&= \int_{0}^{\infty} ye^{-y}\sum_{k=0}^{\infty}k\frac{y^k}{k!}Ae^{-Ay}dy \
&= \int_{0}^{\infty} ye^{-y}\sum_{k=1}^{\infty}\frac{y^{k-1}}{(k-1)!}Ae^{-Ay}dy \
&= A\int_{0}^{\infty} y\sum_{k=1}^{\infty}\frac{(Ay)^{k-1}}{(k-1)!}e^{-Ay}e^{-y}dy \ &= A\int_{0}^{\infty} y\sum_{k=0}^{\infty}\frac{(Ay)^{k}}{k!}e^{-Ay}e^{-y}dy \
&= A\int_{0}^{\infty} ye^{-(A+1)y}\sum_{k=0}^{\infty}\frac{(Ay)^{k}}{k!}dy \
&= A\int_{0}^{\infty} ye^{-(A+1)y}e^{Ay}dy \
&= \frac{A}{(A+1)^2} \end{align*}
Similarly, we can find $E[X^2Y]$ as:
\begin{align*}
E[X^2Y] &= \int_{0}^{\infty} E[X^2Y|Y=y]f_Y(y)dy \
&= \int_{0}^{\infty} E[X^2y]Ae^{-Ay}dy \
&= \int_{0}^{\infty} y^2e^{-y}\sum_{k=0}^{\infty}k^2\frac{y^k}{k!}Ae^{-Ay}dy \
&= \int_{0}^{\infty} y^2e^{-y}\sum_{k=2}^{\infty}\frac{k(k-1)y^{k-2}}{(k-2)!}Ae^{-Ay}dy \
&= A\int_{0}^{\infty} y^2\sum_{k=0}^{\infty}\frac{(Ay)^{k}}{k!}e^{-Ay}e^{-y}dy \ &= A\int_{0}^{\infty} y^2e^{-(A+1)y}\sum_{k=0}^{\infty}\frac{(Ay)^{k}}{k!}dy \
&= A\int_{0}^{\
For such more questions on Probability density function:
https://brainly.com/question/28705601
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What is 631.051 as a fraction
sorry if that doesnt make sense.
Answer:
631 and 51/1000
Step-by-step explanation:
The altitude of an airplane is decreasing at a rate of 40 feet per second. What is the change in altitude of the airplane over a period of 20 seconds?
Answer:
Step-by-step explanation:
-40t
-40(20)
-800 ft
a quadratic polynomial the sum of whose zeros is -3 and product is -10
Answer:
2 and -5 i think
Step-by-step explanation:
Josie makes invitations for her aunt's paper company. Of all the invitations Josie makes, 15/21 are children's party invitations. Of those invitations, 3/5 have an animal on them. What fraction of the invitations Josie makes are children's party invitations with an animal on them?
Answer:
the fraction of the invitations considered to be an animal on them is [tex]\frac{3}{7}[/tex]
Step-by-step explanation:
The computation of the fraction of the invitations considered to be an animal on them is shown below:
= Children party invitations × animal on them
[tex]= \frac{15}{21} \times \frac{3}{5}\\\\= \frac{3}{7}[/tex]
Hence, the fraction of the invitations considered to be an animal on them is [tex]\frac{3}{7}[/tex]
Smiths bike shop rents bikes for $10
plus $4 per hour. Anita paid $22 to
rent a bike. How many hours did
she rent the bike for? Write an
equation to represent this situation
and then solve.
What scale factor was applied to the first rectangle to get the resulting image?
Answer: Another way to look at it is that the rectangle was reduced in a factor of 5 (1/0.2=5)
don't forget to drop a heart hope it helped
Step-by-step explanation:
Answer: 1/0.2=5
Step-by-step explanation:
I hope this helps if you guys need a reach out to me :)
tysmmmmmmmmmmmmmmmmmmmmmm
Answer:
The answer is 10
Step-by-step explanation:
To get this you will make the improper fraction into a fraction and then turn that into decimal form
[tex]4 \frac{1}{8} = 4[/tex]
and
[tex]5 \frac{6}{10} = 6[/tex]
That is how you find the estimated answer
Hope this Helped
que volumen ocupará 600 g de agua?
Answer:
Step-by-step explanation:
600 ml
89+67
berapakah jawapan nya
Answer:
156
Step-by-step explanation
fgcfgvhvcfgvxxbbhhcx
Answer:
Jawapan kepada 89 + 67 = 156
If 95% of students are coming to school tomorrow, what is the complement?
Question 5 options:
A. 95%
B. 100%
C. 1%
D. 5%
Answer:
d
Step-by-step explanation:
can you help me with this question According to Frost in his poem "The Road Not Taken," what kind of difference did taking one road over another road make? A. It made a good difference, B. It made a bad diference, c. Frost does not say
Answer:
the answer is d
Step-by-step explanation:
it only takes 5% to get to 100%
E = MV^2 ÷ 2 + mgh, Make V Subject of the formula
Answer:
[tex] \red{ \bold{ V = \sqrt{\frac{2(E - mgh)}{M}}}}[/tex]
Step-by-step explanation:
[tex]E = MV^2 ÷ 2 + mgh \\ \\ E - mgh = MV^2 ÷ 2 \\ \\ 2(E - mgh)= MV^2 \\ \\ \frac{2(E - mgh)}{M}=V^2 \\ \\ \sqrt{\frac{2(E - mgh)}{M}} = V \\ \\ \red{ \bold{ V = \sqrt{\frac{2(E - mgh)}{M}}}}[/tex]
Can someone please tell me what is the solution
Answer:
[tex] \frac{1}{4} \tan {}^{4}(x) + c[/tex]
4. Six numbers are shown.
1.25, -1.5, -0.75,
34,
2 6/8,
5/4
Place each number in its correct location on the number line.
Step-by-step explanation:
sorry i couldn't solve the last and the last second one
Was it helpful?
comment down
If there is any kind of suspicious mistake
then sorry
How do you solve for x and y?
Answer:
x = 100, y = 50
Step-by-step explanation:
Make a system of equations:
First, you know that x + y degrees and 30 degrees are on a line together, they add up to 180 degrees:
x + y + 30 = 180
x + y = 150
Next, the interior angles of a triangle always add up to 180 degrees, and since 2y, x/2, and 30 are all the angles in a triangle, you have:
2y + x/2 + 30 = 180
x/2 + 2y = 150
Now, all you have to do is solve the system of equations.
To start, multiply the second equation by 2 to get rid of the fraction:
x + 4y = 300
Then, you can subtract the two equations:
x + 4y = 300
- (x + y = 150)
3y = 150
divide both sides by 3
y = 50
substitute y = 50 into the equation x + y = 150:
x + 50 = 150
x = 100
pls help ty !
question is in the pic
Answer:
He is not correct
Please help me 15 points it’s worth it please help me on this question
Answer:
last answer
Step-by-step explanation:
10.
Write a rule for the linear function in the graph.
A. y = 4/5x + 2
B. y = -5x - 2
C. y = 5/4x - 2
D. y = -4/5x + 2
Answer:
D. y = -4/5x + 2
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope:
−
4
5
y-intercept:
(
0
,
2
)
x
y
0
2
5
2
0
Due in 20 please help
The polygons are similar. Find the values of
the variables. Write an equation and solve,
showing ALL the work.
It tells you they are similar. This means the angles are the same, and the sides are proportionate.
Look at the 12 and 4 at the very bottom. This tells you the ratio of the sides. Since 12 / 4 = 3, you can find y with 2 * 3 which is 6.
From that, you also know that 3z = 3y - 2. Substitute the value of y in and you can find z.
Corresponding angles are exactly the same. which means, (3x)° = 100°
You should get x = 33 1/3, y = 6, z = 5 1/3
Hi! PLS HELP ITS 30 POINTS!! Thanks!
A soda bottle holds 1.5 liters of soda. How many milliliters does the bottle hold?
15 millimeters
150 millimeters
1,500 millimeters
15,000 millimeters
Pls help!
Imma report u if its something off the topic!
Thanks again!
(its not b i tried it and got it wrong!! )
Answer:
1,500 millimeters
Step-by-step explanation:
1 litre = 1000 millilitre.
Try 1,500.
What is the scientific notation for .000472
Answer:
The scientific notation for 0.000472 is 4.72 * [tex]10^{-4}[/tex].
solve each system of eaquasions x+4y=4 -x+2y=8
Answer:
(-4, 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/CoefficientsCoordinates (x, y)Solving systems of equations using systemsStep-by-step explanation:
Step 1: Define Systems
x + 4y = 4
-x + 2y = 8
Step 2: Rewrite Systems
x + 4y = 4
[Subtraction Property of Equality] Subtract 4y on both sides: x = 4 - 4yStep 3: Redefine Systems
x = 4 - 4y
-x + 2y = 8
Step 4: Solve for y
Substitution
Substitute in x: -(4 - 4y) + 2y = 8[Distributive Property] Distribute negative: -4 + 4y + 2y = 8Combine like terms: -4 + 6y = 8[Addition Property of Equality] Add 4 on both sides: 6y = 12[Division Property of Equality] Divide 6 on both sides: y = 2Step 5: Solve for x
Define original equation: x + 4y = 4Substitute in y: x + 4(2) = 4Multiply: x + 8 = 4[Subtraction Property of Equality] Subtract 8 on both sides: x = -4can someone please help me u can just do 5 and explain please
¿Puede alguien ayudarme? Puedes hacer 5 y explicar por favor.
Answer:
i only can explain until number 7
i am sorry
maybe that help you
Well I need the help in this last question I will mark brain list if you got it right
Answer:
6x−11y+15
Step-by-step explanation:
Distribute the Negative Sign:
=5x−6y+7+−1(−x+5y−8)
=5x+−6y+7+−1(−x)+−1(5y)+(−1)(−8)
=5x+−6y+7+x+−5y+8
Combine Like Terms:
=5x+−6y+7+x+−5y+8
=(5x+x)+(−6y+−5y)+(7+8)
=6x+−11y+15
Answer:
6x−11y+15
I hope I helped!!
Delia takes out a loan to buy a car for $18,000 with an interest rate of 6.5%. The amount of interest Delia will have to pay is $4,680. Write and solve an equation to determine the number of months her loan is for. Show all of your work and explain how you got your number of months.
Answer:
Delia pays $4,680 in 4 months
Step-by-step explanation:
Equation:
18,000 * 6.5% = 1170
4680 ÷ 4 = 1170
So, the answer is 4 months this is the equation.
Hope this helps! :)
An account earns simple interest.
$600 at 5% for 2 years
a.Find the interest earned.
$___
b.Find the balance of the account.
$___
Please answer and give an explanation with your response. I will mark the correct and quickest answer BRAINLIEST!!!
Answer:
600×100/5×2=
6\10=3/5
Answer:
A is $60
B is $660
Step-by-step explanation:
For A, you move the decimal in 5% 2 over so it is 0.05. You then multiply 0.05 by 600, multiply that answer by 2, and you'll get $60.
Sorry I'm not sure how to do B, I looked up the answer to that one.
Christine has her own dog -walking business. She Charges her customers $20 per day to walk their day
Answer:
y= money made
x = amount of dogs walked
equation- y = 20x
for the table name # of dogs walked on the right and money earned on the left.
for the left put 1 2 3 4 5 6 7 and 8
1 goes with 20
2 goes with 40
3 with 60
4 with 80
5 with 100
6 with 120
7 with 140 and
8 with 160
Step-by-step explanation:
Find the volume of the figure.
10 cm
8 cm
10 cm
14 cm
10 cm
8 cm
cubic centimeters
Answer:
60 cm³
Step-by-step explanation:
Step-by-step explanation:
=896000 is the answer
method -10x8x10x14x10x8
️️
Solve by elimination:
9x + 4y = 97
9x + 6y = 123
14
15'
B (5, 13)
(13,5)
D (1, 22)
Answer:
B (5, 13)
Step-by-step explanation:
9x + 4y = 97
9x + 6y = 123
To solve by elimination, we want to eliminate a variable. To do this, we must make one variable cancel out.
First, we can see that both equations have 9x. To cancel out x, we must make one of the 9x's negative. To do this, multiply each term in the equation by -1.
-1(9x + 6y = 123)
-9x - 6y = -123
This is one of your equations. Set it up with your other given equation.
9x + 4y = 97
-9x - 6y = -123
Imagine this is one equation. Since every term is negative, you will be subtracting each term.
9x + 4y = 97
-9x - 6y = -123
___________
0x -2y = -26
-2y = -26
To isolate y further, divide both sides by -2.
y = 13
Now, to find x, plug y back into one of the original equations.
9x + 4(13) = 97
Multiply.
9x + 52 = 97
Subtract.
9x = 45
Divide.
x = 5
Check your answer by plugging both variables into the equation you have not used yet.
-9(5) - 6(13) = -123
-45 - 78 = -123
-123 = -123
Your answer is correct!
(5, 13)
Hope this helps!
GIVING BRAINLIEST!!!
Answer:
i think its 78.5 but the answers not on there the closest one there to it is 76.5 so just put that one
Step-by-step explanation:
Triangles are similar Find the value of x.
Please help Thank you in advanced
Answer:
x=36
Step-by-step explanation:
14/42=12/x
14x=12(42)
14x=504
x=36