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3 years ago

Determine if the following tables from a lineAr equation if so identify the slope otherwise write non linear

Mathematics

1 answer:

mariarad [96]3 years ago

4 0

2)
a*2 + b = 26;
a*(-4) + b = -16;
then, a*6 = 42 => a = 7 => b = 26 -14 => b = 12;

from table, 7*9 + 12 = 63 + 12 = 75, correct;
7*(-8) + 12 = -56 + 12 = -44, correct;

slope = ( -44 + 16) / ( -8 + 4) = ( - 28) / (-4) = 7 = a;

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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

Given: MNFD is a trapezoid.

Rama09 [41]

A trapezoid with legs MN = FD is an isosceles trapezoid.
An isosceles trapezoid has diagonals that are congruent, therefore: MF = ND.
A quadrilateral with diagonals congruent and perpendicular is a square.
In a square, the height coincides with the side.
The area of a square is given by A = s²
Therefore, the area of MNFD is h²

6 0

3 years ago

7/9 - 4/3w = -5/6 <br> what is w

borishaifa [10]

Answer:

w=1 5/24

Step-by-step explanation:

7/9-4/3w=-5/6

-4/3w=-5/6-7/9

-4/3w=-15/18-14/18

-4/3w=-29/18

w=-29/18:(-4/3)

w=29/18*(3/4)

w=29*3/18*4

w=29/6*4

w=29/24

w=1 5/24

4 0

3 years ago

Which expression represents the measure of segment rs? 7x – 3 7x 5 x 5 x – 3

inn [45]

Answer:

the answer is RS=x+5

if I am right mark it as brianliest

3 0

2 years ago

Can someone help me to write the equation? Plss!!

sasho [114]

Answer:

Step-by-step explanation:

Let x be pineapple juice each serving

T be the final juice available

(1) T = 8x+5

(2) T+11 = 12x

Solving simultaneously,

(8x+5)+11 = 12x

8x+16 = 12x

4x = 16

x = 4

7 0

3 years ago

Read 2 more answers