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g let X be a normally distributed random variable with mean 3 and variance 4. a) Let Y = 5X+2. What is the distribution of Y? What are its mean and variance? b) Find P(Y<10). Find P(X<10). c) What is the 99th percentile of the distribution of Y? d) What is the 99th percentile of the distribution of X? e) What is the distribution of W = exp(Y)? What are its mean and variance?

Answers

Answer 1

Answer:

a. Let $F_X(x)$ be the CDF of $X$ . The CDF of $Y$ is

$F_Y(y)=P(Y\le y)=P(5X+2\le y)=P\left(X\le\frac{y-2}5\right)=F_X\left(\frac{y-2}5\right)$

which is to say, $Y$ is also normally distributed, but with different parameters. In particular,

$E[Y]=E[5X+2]=5E[X]+2=17$

$\mathrm{Var}[Y]=\mathrm{Var}[5X+2]=5^2\mathrm{Var}[X]=100$

b. Using the appropriate CDFs, we have

$P(Y<10)=F_Y(10)=F_X\left(\frac{10-2}5\right)=F_X(1.6)\approx0.242$

$P(X<10)=F_X(10)\approx0.9998$

c. The 99th percentile for any distribution $D$ is the value of $d_(0.99)$ such that $P(D\le d_(0.99))=0.99$ , i.e. all values of $d$ below $d_(0.99)$ make up the lower 99% of the distribution.

We have

$P(Y\le y_(0.99))=0.99\implies y_(0.99)\approx40.26$

d. On the other hand, the 99th percentile for $X$ is

$P(X\le x_(0.99))=0.99\implies x_(0.99)\approx7.653$

e. We have

$F_W(w)=P(W\le w)=P\left(e^Y\le w\right)=P(Y\le\ln w)=F_Y(\ln w)$

which suggests that $\ln W$ is normally distributed, or $W$ is log-normally distributed. Recall that the moment-generating function for $Y$ is

$M_Y(t)=\exp\left(17t+\frac{100t^2}2\right)$

But we also have

$M_Y(t)=E[e^(tY)]=E[e^(t\ln W)]=E[W^t]$

Then

$E[W]=M_Y(1)=e^(67)$

and

$E[W^2]=M_Y(2)=e^(234)\implies\mathrm{Var}[W]=E[W^2]-E[W]^2=e^(234)-e^(134)$

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A principle of $4570 is placed into account that earns 4.5 interest if the interest is compounded annually how much money will be in the account

Answers

Answer:

205.65 interest

Step-by-step explanation:

Answer:

Option D on Edg.

Step-by-step explanation: I took the test and the correct option is $5695.05.

In art class students are mixing blue and red paint to make purple paint. Cai mixes 5 cups of blue paint and 6 cups of red paint. Casho mixes 2 cups of blue paint and 3 cups of red paint. Use Cai and Casho’s percent of blue paint to determine whose purple paint will be bluer.

Answers

Answer:

Cai's Would Be Bluer

Step-by-step explanation:

Since 2/5 is 40% and 5/11 is 45% Cai's would be bluer!

Final answer:

Cai's paint will be bluer because she used a higher percentage of blue paint (45.45%) in her mix compared to Casho who used 40% blue paint.

Explanation:

In order to determine whose paint mix will be bluer, we must compare the ratio of blue to red paint in each student's mix. Cai mixes 5 cups of blue and 6 cups of red paint. Casho mixes 2 cups of blue and 3 cups of red paint. We find the percentage of blue paint by dividing the amount of blue paint by the total amount of paint and then multiplying by 100. For Cai, it would be (5 / (5 + 6)) * 100 = 45.45% blue. For Casho, it would be (2 / (2 + 3)) * 100 = 40% blue. Thus, Cai's purple paint will be bluer because it has a higher percentage of blue paint.

Learn more about Percentage here:

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Considere as mesas com 4 cadeiras, com 6 cadeiras e com 8 cadeiras. ©Shutterstock/jenjira Com base nessa sequência de imagens, qual expressão indica a quantidade de cadeiras utilizadas ao colocarmos n mesas lado a lado?

Answers

Responder:

C. Tₙ = 2n + 2

Explicación paso a paso:

De la pregunta, la secuencia de imágenes, cuya expresión indica es 4 cadeiras, 6 cadeiras, 8 cadeiras ...

Se puede ver la secuencia una progresión aritmética de la forma 4, 6, 8 ... Para obtener la expresión que indica la cantidad de cadenas utilizadas o colocaremos n tablas una al lado de la otra, tendremos que encontrar el enésimo término de la secuencia que usa la fórmula para encontrar el enésimo término de una secuencia aritmética.

El enésimo término de un AP se expresa como Tₙ = a + (n-1) d donde;

a es el primer término

n es el número de términos es la diferencia común

De la secuencia generada, a = 4, d = 6-4 = 8-6 = 2

Tₙ = 4+ (n-1) 2

abre el paréntesis

Tₙ = 4 + 2n-2

Tₙ = 2n + 4-2

Tₙ = 2n + 2

Por lo tanto, la expresión que indica la cantidad de cadenas utilizadas o colocaremos n tablas una al lado de la otra es 2n + 2

A flower delivery driver is 8 1/2 miles west of a city's zoo when she receives a call to pick up flowers from the flower store. The flower store is 14.35 miles east of the zoo. Assume the driver takes the most direct route to the flower store. How will the driver drive to the flower store? Select from the drop-down menus to correctly complete the statement. The driver will drive Choose... miles Choose... .

Answers

Answer: It's 22.85 East

Step-by-step explanation:

Took the test and got a 100%

Answer: 22.85

Step-by-step explanation:

if she starts out 8.5 mile WEST of a zoo, and has to go 14.35 miles EAST of the zoo, then add both of those numbers, and you get, 22.85 miles

I need help on question 6.

Answers

Answer: 135 degrees

Step-by-step explanation:

First you now that ABD+DBC=180 degrees

Subsitute so you get: (5x+10)+(2x-5)=180

Solve:

(5x+10)+(2x-5)=180

=> 7x+5=180

=> 7x=175

=> x= 25

Plug in 25 :

ABD= 5*25+10=135

And there is your answer

Find the limit of the function by using direct substitution. limit as x approaches zero of quantity x squared plus eleven.

Answers

Answer: 11

Step-by-step explanation:

$\displaystyle \lim_(x \to 0) x^2+11 \qquad =(0)^2+11\qquad =\large\boxed{11}$

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