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2 years ago

Which of the following ratios is not equivalent to 6:10? 3/5 9/15 48/80 24/45

1 answer:

4 0

The answer is 24/45

Let's check out all choices:
a) 6:10 = 3:5
6 * 5 = 10 * 3
30 = 30
Therefore, equivalent!

b) 6:10 = 9:15
6 * 15 = 10 * 9
90 = 90
Therefore, equivalent!

c) 6:10 = 48:80
6 * 80 = 10 * 48
480 = 480
Therefore, equivalent!

d) 6:10 = 24:45
6 * 45 = 10 * 24
270 ≠ 240
<u>Therefore, inequivalent!</u>

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If X is a r.v. such that E(X^n)=n! Find the m.g.f. of X,Mx(t). Also find the ch.f. of X,and from this deduce the distribution of

astraxan [27]

$M_X(t)=\mathbb E(e^{Xt})$
$M_X(t)=\mathbb E\left(1+Xt+\dfrac{t^2}{2!}X^2+\dfrac{t^3}{3!}X^3+\cdots\right)$
$M_X(t)=\mathbb E(1)+t\mathbb E(X)+\dfrac{t^2}{2!}\mathbb E(X^2)+\dfrac{t^3}{3!}\mathbb E(X^3)+\cdots$
$M_X(t)=1+t+t^2+t^3+\cdots$
$M_X(t)=\displaystyle\sum_{k\ge0}t^k=\frac1{1-t}$

provided that $|t|$ .

Similarly,

$\varphi_X(t)=\mathbb E(e^{iXt})$
$\varphi_X(t)=1+it+(it)^2+(it)^3+\cdots$
$\varphi_X(t)=(1-t^2+t^4-t^6+\cdots)+it(1-t^2+t^4-t^6+\cdots)$
$\varphi_X(t)=(1+it)(1-t^2+t^4-t^6+\cdots)$
$\varphi_X(t)=\dfrac{1+it}{1+t^2}=\dfrac1{1-it}$

You can find the CDF/PDF using any of the various inversion formulas. One way would be to compute

$F_X(x)=\displaystyle\frac12+\frac1{2\pi}\int_0^\infty\frac{e^{itx}\varphi_X(-t)-e^{-itx}\varphi_X(t)}{it}\,\mathrm dt$

The integral can be rewritten as

$\displaystyle\int_0^\infty\frac{2i\sin(tx)-2it\cos(tx)}{it(1+t^2)}\,\mathrm dt$

so that

$F_X(x)=\displaystyle\frac12+\frac1{2\pi}\int_0^\infty\frac{\sin(tx)-t\cos(tx)}{t(1+t^2)}\,\mathrm dt$

There are lots of ways to compute this integral. For instance, you can take the Laplace transform with respect to $x$ , which gives

$\displaystyle\mathcal L_s\left\{\int_0^\infty\frac{\sin(tx)-t\cos(tx)}{t(1+t^2)}\,\mathrm dt\right\}=\int_0^\infty\frac{1-s}{(1+t^2)(s^2+t^2)}\,\mathrm dt$
$=\displaystyle\frac{\pi(1-s)}{2s(1+s)}$

and taking the inverse transform returns

$F_X(x)=\dfrac12+\dfrac1\pi\left(\dfrac\pi2-\pi e^{-x}\right)=1-e^{-x}$

which describes an exponential distribution with parameter $\lambda=1$ .

6 0

2 years ago

I'LL GIVE THE BRAINLIEST!

ddd [48]

Answer:12 -6 A prime point B -18-9

Step-by-step explanation:

9 divided by 11 is 37 times 17 which is 94

4 0

2 years ago

Read 2 more answers

How to order -14.4, -14, -14 1/5 from least to greatest

ElenaW [278]

Think of thermometer the negative degrees are the coldest so are the lowest on the vertical column

first convert -14 1/5 to decimals = -14.2

so the order is

-14.4 , -14 1/5 , -14.

8 0

2 years ago

In a mathematics class, half of the students scored 87 on an achievement test.

Nimfa-mama [501]

The complete question is:

In a mathematics class, half of the students scored 87 on an achievement test. With the exception of a few students who scored 52, the remaining students scored 71. Which of the following statements is true about the distribution of scores?

A. The mean is less than the median.

B. The mean and the median is the same.

C. The mean is greater than the mode.

D. The mean is greater than the median.

Statistics exist in the analysis of collection, analysis, interpretation, and presentation of data or into discipline to collect and summarize the data.

Therefore, the correct answer is option A. The mean is less than the median.

<h3>What are statistics?</h3>

Statistics exist in the analysis of collection, analysis, interpretation, and presentation of data or into discipline to collect and summarize the data.

Half the students scored 87.

The next highest score exists at 71.

Then the median will be (71+ 87) / 2 = 79

A few students scored 52, so the mean exists a little lower than the mean of 71 and 87.

Therefore, the correct answer is option A. The mean is less than the median.

To learn more about statistics refer to:

brainly.com/question/10951564

#SPJ9

3 0

11 months ago

25<br> 2<br> In long division

Andre45 [30]

Answer:

..........

Step-by-step explanation:

i don't understand 25 2 ??

3 0

2 years ago