Recent content by Linder88

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 LTI (A,B,C,D) system $$ \dot{x}= \begin{pmatrix} 0.5&0&0&0\\ 0&-2&0&0\\ 1&0&0.5&0\\ 0&0&0&-1 \end{pmatrix} x+ \begin{pmatrix} 1\\ 1\\ 0\\ 0 \end{pmatrix} u $$ $$ y= \begin{pmatrix} 0&1&0&1 \end{pmatrix} x $$ Determine if A is diagonalizable Homework EquationsThe...

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...

Are you suggesting somethin like in the equation under? \begin{equation} P(A\cap B)=P(B)P(A|B) \end{equation}

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}

Well, the whole question reads like in the attached picture but I already did the first part!

My teacher told they are not independent even though I wish they were :frown:

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...