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Dmitry_Shevchenko [17]

2 years ago

7

The box plots show the average wind speeds, in miles per hour, for various cities in two different countries

2 answers:

kolezko [41]2 years ago

4 0

In my choice i would choose “the median wind speed for country B is greater than the median wind speed for country A”

DerKrebs [107]2 years ago

3 0

Answer:

B

Step-by-step explanation:

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1. Which solid has one base that is a rectangle and four lateral surface that are triangles?

Ber [7]

1. Triangular prism
2. Sphere i think

7 0

2 years ago

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

Describe the likelihood of an event as impossible, unlikely, equally likely, likely or certain. 21) There is a 0% chance of pick

Arturiano [62]

Answer:

21) There is a 0% chance of picking a 13 in a deck of cards. <u>Impossible.</u>

If there is a 0% chance that something will happen then it is impossible.

22) There is a 50% chance of picking a red card in a deck of cards.<u> Equally likely.</u>

If there is a 50% chance that something will happen, it is equally likely that it will happen.

23) There is an 80% chance of snow tomorrow. <u>Likely or certain.</u>

If there is an 80% chance of something happening, it means that the chances of that thing happening good and the event is likely to occur.

24) There is a 20% chance of rain tomorrow. <u>Unlikely.</u>

A low chance of 20% means that something is unlikely to occur.

7 0

2 years ago

[NO WRONG ANSWERS!!!]<br><br> What is the sum of the following equation?<br><br> 89x+5y+1x+5y

mixas84 [53]

Answer:

90x+10y

Step-by-step explanation:

Add 89 and 1

Add 5 and 5

90x+10y in this order

3 0

2 years ago

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Montano1993 [528]

<span>To which set of numbers does −1.2 belong? </span>D.) rational numbers

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2 years ago