You can write out the equation like so: t = 2(d) and the dvd costs d. So, d + 2d = 1296. Which is also 3D=1296. So divide 1296/3 to solve for the cost of the DVD player = 432 and the cost of the tv is 2(d) or 2 x 432 = 864.
I know you said "without making any assumptions," but this one is pretty important. Assuming you mean
are shape/rate parameters (as opposed to shape/scale), the PDF of
is

if
, and 0 otherwise.
The MGF of
is given by
![\displaystyle M_X(t) = \Bbb E\left[e^{tX}\right] = \int_{-\infty}^\infty e^{tx} f_X(x) \, dx = \frac{2^8}{\Gamma(8)} \int_0^\infty x^7 e^{(t-2) x} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20M_X%28t%29%20%3D%20%5CBbb%20E%5Cleft%5Be%5E%7BtX%7D%5Cright%5D%20%3D%20%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20e%5E%7Btx%7D%20f_X%28x%29%20%5C%2C%20dx%20%3D%20%5Cfrac%7B2%5E8%7D%7B%5CGamma%288%29%7D%20%5Cint_0%5E%5Cinfty%20x%5E7%20e%5E%7B%28t-2%29%20x%7D%20%5C%2C%20dx)
Note that the integral converges only when
.
Define

Integrate by parts, with


so that

Note that

By substitution, we have

and so on, down to

The integral of interest then evaluates to

so the MGF is

The first moment/expectation is given by the first derivative of
at
.
![\Bbb E[X] = M_x'(0) = \dfrac{8\times\frac12}{\left(1-\frac t2\right)^9}\bigg|_{t=0} = \boxed{4}](https://tex.z-dn.net/?f=%5CBbb%20E%5BX%5D%20%3D%20M_x%27%280%29%20%3D%20%5Cdfrac%7B8%5Ctimes%5Cfrac12%7D%7B%5Cleft%281-%5Cfrac%20t2%5Cright%29%5E9%7D%5Cbigg%7C_%7Bt%3D0%7D%20%3D%20%5Cboxed%7B4%7D)
Variance is defined by
![\Bbb V[X] = \Bbb E\left[(X - \Bbb E[X])^2\right] = \Bbb E[X^2] - \Bbb E[X]^2](https://tex.z-dn.net/?f=%5CBbb%20V%5BX%5D%20%3D%20%5CBbb%20E%5Cleft%5B%28X%20-%20%5CBbb%20E%5BX%5D%29%5E2%5Cright%5D%20%3D%20%5CBbb%20E%5BX%5E2%5D%20-%20%5CBbb%20E%5BX%5D%5E2)
The second moment is given by the second derivative of the MGF at
.
![\Bbb E[X^2] = M_x''(0) = \dfrac{8\times9\times\frac1{2^2}}{\left(1-\frac t2\right)^{10}} = 18](https://tex.z-dn.net/?f=%5CBbb%20E%5BX%5E2%5D%20%3D%20M_x%27%27%280%29%20%3D%20%5Cdfrac%7B8%5Ctimes9%5Ctimes%5Cfrac1%7B2%5E2%7D%7D%7B%5Cleft%281-%5Cfrac%20t2%5Cright%29%5E%7B10%7D%7D%20%3D%2018)
Then the variance is
![\Bbb V[X] = 18 - 4^2 = \boxed{2}](https://tex.z-dn.net/?f=%5CBbb%20V%5BX%5D%20%3D%2018%20-%204%5E2%20%3D%20%5Cboxed%7B2%7D)
Note that the power series expansion of the MGF is rather easy to find. Its Maclaurin series is

where
is the
-derivative of the MGF evaluated at
. This is also the
-th moment of
.
Recall that for
,

By differentiating both sides 7 times, we get

Then the
-th moment of
is

and we obtain the same results as before,
![\Bbb E[X] = \dfrac{(k+7)!}{7!\,2^k}\bigg|_{k=1} = 4](https://tex.z-dn.net/?f=%5CBbb%20E%5BX%5D%20%3D%20%5Cdfrac%7B%28k%2B7%29%21%7D%7B7%21%5C%2C2%5Ek%7D%5Cbigg%7C_%7Bk%3D1%7D%20%3D%204)
![\Bbb E[X^2] = \dfrac{(k+7)!}{7!\,2^k}\bigg|_{k=2} = 18](https://tex.z-dn.net/?f=%5CBbb%20E%5BX%5E2%5D%20%3D%20%5Cdfrac%7B%28k%2B7%29%21%7D%7B7%21%5C%2C2%5Ek%7D%5Cbigg%7C_%7Bk%3D2%7D%20%3D%2018)
and the same variance follows.
Answer:
52.6,56.6,594.3
Step-by-step explanation:
you multiply all o them
If you are in a school app similar to mine you drag your mouse over the line look for the 1 the one has to be first number. There will be 2 numbers it will look like (1,?) the second number is unknown so look for it and type it in
Answer: 
Step-by-step explanation:
the conjugate is:
