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3 years ago

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The truth table represents statements p, q, and r. p q r A T T T B T T F C T F T D T F F E F T T F F T F G F F T H F F F Which s

tatements are true for rows A and E? Check all that apply. p ↔ q p ↔ r q ↔ p q ↔ r r ↔ p r ↔ q

2 answers:

o-na [289]3 years ago

8 0

Answer:

r--(pvq)

Step-by-step explanation:

just did the review

Lina20 [59]3 years ago

4 0

We have been given the truth table for three variables p, q, and r. as shown below

p q r

A T T T

B T T F

C T F T

D T F F

E F T T

F F T F

G F F T

H F F F

Now we need to find Which statements are true for rows A and E for the following statements:

p ↔ q p ↔ r q ↔ p q ↔ r r ↔ p r ↔ q

To find that we need to use table of P <-> Q as shown in picture.

We know that if both statements are true for P and Q then only P <-> Q will be true. So using that trick we see that only q<->r and r<->q are the final answer as shown in the attached picture.

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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

What is 35x 1 ? OMG this is such a hard question!! first one to answer will get a brainliest!!!

bagirrra123 [75]

Answer:

35 x 1 = 35

Step-by-step explanation:

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2 years ago

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The perimeter of rectangle living room is 40 m the living room is 10 m wide what is the length of the living room

Yuri [45]

Answer:

Width of the room = 5 meters

Step-by-step explanation:

the rectangular living room is calculated as length * width

The area is given to be equal to 40 sq. meters (area = 40 sq. meters)

Let the width = x meters

Length = X+3 meters

Area = Length * Width

40 = X * (X+3)

40 = X^2 + 3X

We solve this quadratic equation

So x = 5 or x= -8

Width cannot be negative, so we reject x =-8

So x = 5 is the answer

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2 years ago

Jasmine purchased a laptop worth $1,500 in 2007. It loses its value by %32 each year. What is the value of the laptop in 2010? R

Lunna [17]

Answer:

$471.65

Step-by-step explanation:

-The value of the laptop after each year is calculated by the formula:

$P_t=P_o(1-d)^t$

where:

$P_t$ is the value at time t

$P_o$ is the initial value

$d$ is the rate of depreciation

$t$ is the time

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Hence, the value of the laptop in 2010 is $471.65

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A doctor's office has a computer file showing the heights of 100 male patients of one of the doctors of the practice. the height

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A) Yes. we don't have enough information so this can not be determined.
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