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1 year ago

Takeout orders on a typical saturday

Mathematics

1 answer:

erma4kov [3.2K]1 year ago

6 0

Value is that you are the most important person to your mom

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chegg Y=4X−2 XX has a PDF of f_X(x)=\begin{cases} 3e^{-3x} & 0 \leq x \\ 0 & \text{otherwise}\end{cases}f X (x)={ 3e −

Licemer1 [7]

$\Bbb E[Y^2] = \Bbb E[(4X - 2)^2]$

so by definition of expectation,

$\Bbb E[Y^2] = \displaystyle \int_{-\infty}^\infty (4x-2)^2 f_X(x) \, dx = \int_0^\infty 3(4x-2)^2 e^{-3x} \, dx$

Integrate by parts (twice).

$\displaystyle \int_a^b u\,dv = uv\bigg|_a^b - \int_a^b v\,du$

First, let

$u = (4x-2)^2 \implies du = 8(4x-2)\,dx \\\\ dv = 3e^{-3x} \, dx \implies v = -e^{-3x}$

so that

$\displaystyle \Bbb E[Y^2] = -(4x-2)^2 e^{-3x} \bigg|_{x=0}^{x\to\infty} + 8 \int_0^\infty (4x-2) e^{-3x} \, dx \\\\ ~~~~ = 4 + 8 \int_0^\infty (4x-2) e^{-3x} \, dx$

Next,

$u = 4x-2 \implies du = 4\,dx \\\\ dv = e^{-3x} \, dx \implies v = -\dfrac13 e^{-3x}$

so that

$\displaystyle \Bbb E[Y^2] = 4 + 8 \left(-\frac13 (4x-2) e^{-3x} \bigg|_{x=0}^{x\to\infty} + \frac43 \int_0^\infty e^{-3x} \, dx\right) \\\\ ~~~~ = 4 + 8 \left(-\frac23 - \frac49 e^{-3x}\bigg|_{x=0}^{x\to\infty}\right) \\\\ ~~~~ = 4 - \frac{16}3 + \frac{32}9 = \boxed{\frac{20}9}$

7 0

11 months ago

Pls help me! i’m very confused on this certain question.

Vitek1552 [10]

Answer:

Step-by-step explanation:

scientific notation always contains a decimal number

7 0

2 years ago

Guys plz help me answer this !!!!

Stella [2.4K]

Answer: -1

Step-by-step explanation:

8-13=s+4s

-5=5s

-5/5=5s/5

-1=s

5 0

2 years ago

Read 2 more answers

Write an equation to express the relationship between pressure and temperture (k) use the symbols p,t,k

IRISSAK [1]

K = constant

k * temperature = pressure

or p/t = k

this is gay-lussac's law. are you using temperature in kelvin or is that a mistake while writing the question?

6 0

2 years ago

Someone please help??

Xelga [282]

Answer:

x-axis

Step-by-step explanation:

The asymptote is a straight line that the curve gets closer and closer to but never touches it.

The given exponential function is $f(x)=3^x$ .

The given graph has a horizontal asymptote,

The equation of this horizontal asymptote is y=0.

This is also refers to as the x-axis.

Therefore the asymptote is the x-axis.

6 0

2 years ago