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2 years ago

Could anyone help me out with this?

Mathematics

1 answer:

Mama L [17]2 years ago

7 0

Answer: they are abt the same its all abt percentage now- Pitcher A

Step-by-step explanation: more water lessens the strength

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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

What is 70% of 50? explain how you got this answer.

eimsori [14]

First, convert the percent into a decimal. You can make any percent into a decimal by moving the % sign two places to the left and making it into a decimal point.

70% = 0.70

In mathematics, if can also mean multiply.

0.70 * 50 = 35

So, 35 is the answer to this question.

7 0

3 years ago

Read 2 more answers

Enter your answer and show all the steps that you use to solve this problem in the space provided. What is the value of x?

WINSTONCH [101]

Answer:

x = 71°

Step-by-step explanation:

because the triangle shown in the image is an isosceles if the top angle is 38 the sum of other two angles must be 142 which is ,if divided by 2, makes 71

7 0

3 years ago

Read 2 more answers

What is the value of x in the solution to the following system of linear equations? Y=3x+2 y=x-4

omeli [17]

Answer:-3

Step-by-step explanation:

y=3x+2................(1)

y=x-4......................(11)

Subtract (11) from (1)

y-y=3x-x+2-(-4)

0=2x+2+4

0=2x+6

Collect like terms

0-6=2x

-6=2x

Divide both sides by 2

-6/2=2x/2

-3=x

x=-3

5 0

3 years ago

Tracy solved the following problem. Which of the statements is true?

Inessa [10]

it would be the third answer choice, when doing this you always make sure that there is multiplication or division you do those first going left to right, even if there is addition first, you still would do either multiplication or division first.

7 0

2 years ago