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2 years ago

Express the following in the form of p/q where p and q are integers and q is not equal to 0.

Mathematics

2 answers:

ANEK [815]2 years ago

3 0

Answer:

1.06bar is not equal to zero

slava [35]2 years ago

3 0

The answer is 1 0.06

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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 $\lambda=1$ .

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3 years ago

The hanger image below represents a balanced equation

olchik [2.2K]

Answer: A

Step-by-step explanation:

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2 years ago

It took a car 6 hours to cover the distance between points A and B with the speed of 50 mph. How long will it take a bus to cove

Leno4ka [110]

Answer:

7hours and 30 minutes

Step-by-step explanation:

given a car travels with a speed of 50 miles -------->1hour

x miles -------->6hours

on cross multiplying we get the value of 'x'

x = 50×6 = 300

x=300miles

Now ,

40mls------->1h

300mls------->xh

x= 300/40

x=(3/4)×10

x= 7.5hours

x= 7½hours

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2 years ago

PLZ help 50 pts. and brainliest

olganol [36]

Answer:

what do u want us to do?

Step-by-step explanation:

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3 years ago

Mr. Khans is buying staplers for his office. Each stapler costs $16.99. Write A Function to Represent this situation.

Ksenya-84 [330]

Since each stapler costs 16.99, the total cost is 16.99*x, with x representing the number of staplers bought. This works due to that he adds 16.99 for every stapler, and multiplying it adds 16.99 each time he buys a new stapler

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3 years ago

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