We choose an approximative solution given by
$$
u_N(x) = \frac{a_0}{2} + \sum_{n=1}^N a_n \cos nx + b_n \sin nx
$$
Comparing this approximative solution with the differential equation yields that
$$
\frac{a_0}{2} = a
$$
and the boundary conditions yields the equation system
$$
a + \sum_{n=1}^N...
Yes, you are right. I realized that I have misunderstood the quetion, I'm supposed to first tale the inverse of $G(z)$
$$
1. G^{-1}(z)=\frac{1}{G(z)}=1-\alpha z^{-1} \\
2. G^{-1}(z)=\frac{1}{1-z^{-1}} \\
3. G^{-1}(z)=\frac{1-\alpha z^{-1}}{\alpha-z^{-1}}
$$
Now, I only need to make the inverse...
Homework Statement
The assignment is to find a closed-form expression for the FIR least squares inverse filter of length N for each of the following systens
Homework Equations
$$
1.G( z ) = \frac{1}{1 - \alpha z^{-1}}; | \alpha | < 1 \\
2. G(z) = 1 - z^{-1} \\
3. G(z) = \frac{\alpha -...
Homework Statement
Consider the differential equation
\begin{equation}
y'''-y''=u
\end{equation}
Discretize (1) using a forward-Euler scheme with sampling period
\begin{equation}
\Delta=1
\end{equation}
and find the transfer function between u(k) and y(k)
Homework Equations
The Euler method is...
I think i finally get it. For a given pair i would have that
$$
F_{XY}(x,y)=
\begin{cases}
0,x<0,y<0\\
0.2+0.1,0\leq x<1,0\leq y<1\\
0.2+0.1+0.3,0\leq x<1,1\leq y<2\\
0.2+0.1+0.3+0.1,1\leq x<2,1\leq y<2\\
0.2+0.1+0.3+0.1+0.2+0.1,1\leq x,2\leq y
\end{cases}
$$
or
$$
F_{XY}(x,y)=
\begin{cases}...
The shaded area is a inverted triangle in the upper half of the plane with y vertical and x horizontal, so we have that
$$
P(X<Y|x>0)=\frac{\int_0^1\int_{-y}^y4|xy|dxdy}{\int_0^12xdx}=\frac{1}{1}=1
$$
I guess this concludes this topic, thanks :)
Homework Statement
Determine ##P(X<Y|x>0)##
Homework Equations
X and Y are random variables with the joint density function
$$
f_{XY}(x,y)=
\begin{cases}
4|xy|,-y<x<y,0<y<1\\
0,elsewhere
\end{cases}$$
The marginal densities are given by
$$
f_X(x)=2x\\
f_Y(y)=4y^3
$$
The Attempt at a Solution...
So
\begin{equation}
P(T\geq 10| T>5)=\frac{P(T\geq 10)}{1-P(T\leq 5)}
\end{equation}
The probability that the traveller will have to wait at least 10 minutes
\begin{equation}
P(T\geq 10)=\int_{10}^{\infty}f_T(t)dt=\int_{10}^{20}\frac{1}{20}dt=\frac{1}{2}
\end{equation}
the probability that the...
I don't understand why you have to be so mysterious about the answer, this is not a homework question in that sense. It is a question from my last exam which I'm trying to figure out what I did wrong. To be totally honest I don't understand what you mean, English is not my first language, nor my...
I guess you mean
\begin{equation}
F_{XY}(x,y)=
\begin{cases}
(0.2+0.3+0.1)(0.2+0.1),x=0;y=0\\
(0.2+0.1+0.1)(0.3+0.1),x=1;y=1\\
0.2+0.1,y=2
\end{cases}
\end{equation}
Okey, thanks for the replies. Using your advices leads me to
\begin{equation}
P(T\geq 10|T>5)=\frac{P(T\geq 10\cap T>5)}{P(T>5)}=\frac{F_T(T\geq 10)F_T(T>5)}{F_T(T>5)}\\
=F_T(T\geq 10)=\frac{10}{20}=\frac{1}{2}
\end{equation}
I know this isn't rigth but I can't handle the fact that they are...