Please help! Find the equation of the line that passes through the point (6, 11) and is parallel to y = 2/3 x

Jake is building a fence around his property. He wants the perimeter to be no more than 100 feet. He also wants the length to be

matrenka [14]

Answer:10 feet

Step-by-step explanation:

3 0

3 years ago

If X and Y are independent continuous positive random

Leni [432]

a) $Z=\frac XY$ has CDF

$F_Z(z)=P(Z\le z)=P(X\le Yz)=\displaystyle\int_{\mathrm{supp}(Y)}P(X\le yz\mid Y=y)P(Y=y)\,\mathrm dy$

$F_Z(z)\displaystyle=\int_{\mathrm{supp}(Y)}P(X\le yz)P(Y=y)\,\mathrm dy$

where the last equality follows from independence of $X,Y$ . In terms of the distribution and density functions of $X,Y$ , this is

$F_Z(z)=\displaystyle\int_{\mathrm{supp}(Y)}F_X(yz)f_Y(y)\,\mathrm dy$

Then the density is obtained by differentiating with respect to $z$ ,

$f_Z(z)=\displaystyle\frac{\mathrm d}{\mathrm dz}\int_{\mathrm{supp}(Y)}F_X(yz)f_Y(y)\,\mathrm dy=\int_{\mathrm{supp}(Y)}yf_X(yz)f_Y(y)\,\mathrm dy$

b) $Z=XY$ can be computed in the same way; it has CDF

$F_Z(z)=P\left(X\le\dfrac zY\right)=\displaystyle\int_{\mathrm{supp}(Y)}P\left(X\le\frac zy\right)P(Y=y)\,\mathrm dy$

$F_Z(z)\displaystyle=\int_{\mathrm{supp}(Y)}F_X\left(\frac zy\right)f_Y(y)\,\mathrm dy$

Differentiating gives the associated PDF,

$f_Z(z)=\displaystyle\int_{\mathrm{supp}(Y)}\frac1yf_X\left(\frac zy\right)f_Y(y)\,\mathrm dy$

Assuming $X\sim\mathrm{Exp}(\lambda_x)$ and $Y\sim\mathrm{Exp}(\lambda_y)$ , we have

$f_{Z=\frac XY}(z)=\displaystyle\int_0^\infty y(\lambda_xe^{-\lambda_xyz})(\lambda_ye^{\lambda_yz})\,\mathrm dy$

$\implies f_{Z=\frac XY}(z)=\begin{cases}\frac{\lambda_x\lambda_y}{(\lambda_xz+\lambda_y)^2}&\text{for }z\ge0\\0&\text{otherwise}\end{cases}$

and

$f_{Z=XY}(z)=\displaystyle\int_0^\infty\frac1y(\lambda_xe^{-\lambda_xyz})(\lambda_ye^{\lambda_yz})\,\mathrm dy$

$\implies f_{Z=XY}(z)=\lambda_x\lambda_y\displaystyle\int_0^\infty\frac{e^{-\lambda_x\frac zy-\lambda_yy}}y\,\mathrm dy$

I wouldn't worry about evaluating this integral any further unless you know about the Bessel functions.

6 0

3 years ago

Reuben needs 280 programs for the school play on Thursday. How many boxes of programs will he need, given that each box contains

Tresset [83]

The answer would be 8 boxes

4 0

2 years ago

Tubby ate 100 cookies in 5 days.Each day he ate 6 more than the day before. How many cookies did he eat the frist day.

Natasha2012 [34]

He ate 8 cookies the first day

6 0

3 years ago

What is the rate of inflation if an account has a nominal interest rate of 4.2% and a real interest rate of 2.8%

kirza4 [7]

Answer:

Rate of inflation = 1.4%

Step-by-step explanation:

Given:

Nominal interest rate = 4.2%

Real interest rate = 2.8%

Find:

Rate of inflation

Computation:

Rate of inflation = Nominal interest rate - Real interest rate

Rate of inflation = 4.2% - 2.8%

Rate of inflation = 1.4%

8 0

3 years ago

Please help! Find the equation of the line that passes through the point (6, 11) and is parallel to y = 2/3 x - 5