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2 years ago

Anyone know what 1 and 2 pls help will give brainliest

Mathematics

1 answer:

Reika [66]2 years ago

3 0

Answer:

no se ve

Step-by-step explanation:

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The lifetime X (in hundreds of hours) of a certain type of vacuum tube has a Weibull distribution with parameters α = 2 and β =

stich3 [128]

I'm assuming $\alpha$ is the shape parameter and $\beta$ is the scale parameter. Then the PDF is

$f_X(x)=\begin{cases}\dfrac29xe^{-x^2/9}&\text{for }x\ge0\\\\0&\text{otherwise}\end{cases}$

a. The expectation is

$E[X]=\displaystyle\int_{-\infty}^\infty xf_X(x)\,\mathrm dx=\frac29\int_0^\infty x^2e^{-x^2/9}\,\mathrm dx$

To compute this integral, recall the definition of the Gamma function,

$\Gamma(x)=\displaystyle\int_0^\infty t^{x-1}e^{-t}\,\mathrm dt$

For this particular integral, first integrate by parts, taking

$u=x\implies\mathrm du=\mathrm dx$

$\mathrm dv=xe^{-x^2/9}\,\mathrm dx\implies v=-\dfrac92e^{-x^2/9}$

$E[X]=\displaystyle-xe^{-x^2/9}\bigg|_0^\infty+\int_0^\infty e^{-x^2/9}\,\mathrm x$

$E[X]=\displaystyle\int_0^\infty e^{-x^2/9}\,\mathrm dx$

Substitute $x=3y^{1/2}$ , so that $\mathrm dx=\dfrac32y^{-1/2}\,\mathrm dy$ :

$E[X]=\displaystyle\frac32\int_0^\infty y^{-1/2}e^{-y}\,\mathrm dy$

$\boxed{E[X]=\dfrac32\Gamma\left(\dfrac12\right)=\dfrac{3\sqrt\pi}2\approx2.659}$

The variance is

$\mathrm{Var}[X]=E[(X-E[X])^2]=E[X^2-2XE[X]+E[X]^2]=E[X^2]-E[X]^2$

The second moment is

$E[X^2]=\displaystyle\int_{-\infty}^\infty x^2f_X(x)\,\mathrm dx=\frac29\int_0^\infty x^3e^{-x^2/9}\,\mathrm dx$

Integrate by parts, taking

$u=x^2\implies\mathrm du=2x\,\mathrm dx$

$\mathrm dv=xe^{-x^2/9}\,\mathrm dx\implies v=-\dfrac92e^{-x^2/9}$

$E[X^2]=\displaystyle-x^2e^{-x^2/9}\bigg|_0^\infty+2\int_0^\infty xe^{-x^2/9}\,\mathrm dx$

$E[X^2]=\displaystyle2\int_0^\infty xe^{-x^2/9}\,\mathrm dx$

Substitute $x=3y^{1/2}$ again to get

$E[X^2]=\displaystyle9\int_0^\infty e^{-y}\,\mathrm dy=9$

Then the variance is

$\mathrm{Var}[X]=9-E[X]^2$

$\boxed{\mathrm{Var}[X]=9-\dfrac94\pi\approx1.931}$

b. The probability that $X\le3$ is

$P(X\le 3)=\displaystyle\int_{-\infty}^3f_X(x)\,\mathrm dx=\frac29\int_0^3xe^{-x^2/9}\,\mathrm dx$

which can be handled with the same substitution used in part (a). We get

$\boxed{P(X\le 3)=\dfrac{e-1}e\approx0.632}$

c. Same procedure as in (b). We have

$P(1\le X\le3)=P(X\le3)-P(X\le1)$

and

$P(X\le1)=\displaystyle\int_{-\infty}^1f_X(x)\,\mathrm dx=\frac29\int_0^1xe^{-x^2/9}\,\mathrm dx=\frac{e^{1/9}-1}{e^{1/9}}$

Then

$\boxed{P(1\le X\le3)=\dfrac{e^{8/9}-1}e\approx0.527}$

7 0

2 years ago

PLEASE HELP ASAP ILL GIVE BRAINLY!!!variables & Constants

jolli1 [7]

Independent variables (IV): These are the factors or conditions that you manipulate in an experiment.

Dependent variable It is something that depends on other factors

A constant is a value or number that never changes in expression; it's constantly the same.

A control group in a scientific experiment is a group separated from the rest of the experiment, where the independent variable being tested cannot influence the results.

I hope I was helpful

3 0

2 years ago

Camacho is buying a monster truck. The price of the truck is xxx dollars, and he also has to pay a 13\%13%13, percent monster tr

Anastaziya [24]

Answer:

Camacho pays in total for the monster truck = $x + $0.13x = $1.13x

Step-by-step explanation:

i.) The price of truck is $x

ii.) Monstor truck tax = 13% of price of truck = $\frac{13}{100}\times $x$ = $0.13x

iii) Camacho pays in total for the monster truck = $x + $0.13x = $1.13x

3 0

3 years ago

Evaluate: (4 + 6 • 3) + 3

hichkok12 [17]

Answer:

$25$

Step-by-step explanation:

$(4 + 6 \times 3) + 3$

$=(4 + 18) + 3$

$=(22) + 3$

$=22+3$

$=25$

8 0

2 years ago

Read 2 more answers

Can someone please help me with this

Inessa05 [86]

To find the area of a prism, you calculate the area of the cross-section and multiply that number by the length. The cross-section of this prism is a trapezium, and the formula for this is $\frac{a+b}{2}h$ .
Insert your given numbers to find out the area of this prism's cross-section:
$\frac{3+12}{2}12=90$
Now, multiply 90 by the length, 10cm, to find out the volume of the prism;
90×10=900cm³
Therefore, your answer id the third option.

6 0

3 years ago