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3 years ago

13

Benjamin left his house and drove to the store. He stopped and went inside. From there, he drove in the same direction until he

got to the bank. He stopped and went inside the bank. Then he drove home. The graph below shows the number of blocks away from home Benjamin is xx minutes after he left his house, until he got back home.

1 answer:

Maru [420]3 years ago

7 0

Answer:

whats the question??

Step-by-step explanation:

You might be interested in

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

The product of two Even numbers

krek1111 [17]

The product of two even numbers is even.

Let m and n be any integers so that 2m and 2k are two even numbers.

The product is 2m(2k) = 2(2mk), which is even.

Things to think about:

Why didn’t I just show you by using any two even numbers like the number 4 and the number 26?

Why did I change from "m" to "k" ? Are they really different numbers or could they be the same?

Why did I specifically say that m and k were integers?

The product of two odd numbers is an odd number.

Let m and k be any integers. This means that 2m+1 and 2k+1 are odd numbers.

The product is 4mk + 2m + 2k + 1 (hint: I used FOIL) which can be written as

2 ( 2mk + m + k ) + 1 which is an odd number.

3 0

3 years ago

Recall the chapter example which described the fact that the mean IQ in large, diverse populations is 100 and the standard devia

vova2212 [387]

Answer:

The margin of error for the 99% confidence level for this sample is ±2.23.

None of the given figures is close to the answer:

E. None of the above

Step-by-step explanation:

margin of error (ME) around the mean can be calculated using the formula

ME= $\frac{z*s}{\sqrt{N} }$ where

z is the corresponding statistic of the 99% confidence level (2.576)

s is the population IQ standard deviation (15)

N is the sample size (300)

Using these numbers we get:

ME= $\frac{2.576*15}{\sqrt{300} }$ ≈ 2.23

7 0

3 years ago

17. What expression is equivalent to log(200) - log (2)? Calculate the answer.

IRINA_888 [86]

Answer: 2

Step-by-step explanation:

Recall from the laws of Logarithms:

Log a - Log b = Log ( a/b )

That means

Log 200 - Log 2 = Log ( 200/2)

= Log 100 , which could be written as

Log $10^{2}$

Recall from laws of Logarithms:

Log $a^{b}$ = b Log a

Therefore:

Log $10^{2}$ = 2 Log 10

Also from law of Logarithm

Log 10 = 1

Therefore 2 Log 10 = 2 x 1

= 2

3 0

3 years ago

You need half a liter of milk how many millimeters do you need

never [62]

Proably about 500 milleleters

8 0

3 years ago