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3 years ago

Which function represents a line with a slope of −4 and a y-intercept of −2?

Mathematics

1 answer:

NNADVOKAT [17]3 years ago

5 0

Answer:

y=-4x-2 so c

Step-by-step explanation:

the slope is always gonna be the number that is attached to the x

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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

3 years ago

Sally Jones pays $50.00 a month for group health insurance. There is a $300 deductible. Her medical bills for the last year were

neonofarm [45]

Given

Find out the what was the insurance company's payment .

To proof

As given

Sally Jones pays $50.00 a month for group health insurance

There is a $300 deductible

Her medical bills for the last year were $2,600.00

Linda's insurance company provided payment of 80% of the bills less the deductible.

Deductible

The amount of money you will pay in an insurance claim before the insurance company starts paying you.

medical bill reducing the deductible = $2,600 - $300

= $2300

80 % is written in the decimal form

$= \frac{80}{100}$

= 0.8

than the equation becomes

Linda's insurance company provided payment = 0.8× 2300

= $1840

Therefore the the insurance company's payment be $1840 .

Hence proved

5 0

3 years ago

Please help<br> will give brainliest

nika2105 [10]

i cannot read it swry

7 0

3 years ago

Is the point (1,2) on the graph of f(x)=3x-1 <br>(Show full working)

Maslowich

Answer:

$f(x) = 3x - 1 \\2 = 3(1) - 1 \\ 2 = 2 \\ \therefore \: the \: point \: \binom{1}{2} \: is \: on \: the \\ graph \: of \: f(x) = 3x - 1$

3 0

2 years ago

What is the completely factored form of 20x² – 45

Nina [5.8K]

Answer:

5(2x(2x + 3) - 3 ( 2x +) or 5(2x -3) (2x + 3)

4 0

2 years ago