The joint probability density function of X and Y is given by f(x,y)=67(x2+xy2)0Y}. (d) Find P{Y> \frac { 1 } { 2 } | X < \frac { 1 } { 2 } } , (e) Find E[X]. (f) Find E[Y}.

The joint probability density function of X and Y is given by  f(x,y)=67(x2+xy2)0<x<1,0<y<2 (a) Verify that this is indeed a joint density function. (b) Compute the density function of X. (c) Find P{X>Y}. (d) Find P{Y> \frac { 1 } { 2 } | X < \frac { 1 } { 2 } }

Find the magnetic field intensity (𝐻”βƒ—) for all points in the space for the given current distribution. I, 𝐼, 𝐽’,𝑀, π‘Žπ‘›π‘‘ 𝐾 π‘Žπ‘Ÿπ‘’ π‘π‘œπ‘›π‘ π‘‘π‘Žπ‘‘π‘›π‘‘π‘ . Note that there is no current for 𝜌 > 𝑐 b) Find the magmetic field intensity for just before and after 𝜌 = 𝑏 π‘Žπ‘›π‘‘ 𝜌 = 𝑐 (need to do on – an d + of b and c) c) Examine magentic boundary conditions at 𝜌 = 𝑏 π‘Žπ‘›π‘‘ 𝜌 = 𝑐 For this part you need to set up “”””βƒ— “”””βƒ— 9𝐻: βˆ’ 𝐻<=π‘₯𝑛? 𝑖𝑑𝑒𝑛𝑑𝑖𝑓𝑦 𝑛? 𝑀hπ‘Žπ‘‘ 𝑖𝑠 π‘Žπ‘›π‘‘ 𝑠hπ‘œπ‘€ 𝑖𝑓 𝑑h𝑒 π‘π‘œπ‘’π‘›π‘‘π‘Žπ‘Ÿπ‘¦ π‘π‘œπ‘›π‘‘π‘–π‘‘π‘–π‘œπ‘› π‘€π‘œπ‘Ÿπ‘˜π‘  π‘‘π‘œ 𝑔𝑒𝑑 𝑓𝑒𝑙𝑙 π‘π‘œπ‘–π‘›π‘‘π‘  Finally, please remember H is a vector and need to be clearly show, how you find the magniture and what is the vector in each region

Problem 1 Write MATLAB Program to compute and plot the frequency response of a causal LTI discrete-time system with a transfer function given by for 0 ο‚£  ο‚£  . What type of filter does it represent? H(z) ο€½ 0.15(1ο€­ zο€­2 ) 1ο€­0.5zο€­1 0.7zο€­2 Problem 2 Repeat Problem 2 for the following transfer function: H(z) ο€½ 0.15(1ο€­ zο€­2 ) 0.7ο€­0.5zο€­1 zο€­2 What is the difference between the two filters in problem 1 and problem2, respectively? Which one will you choose for filtering and why? Problem 3 1. Find this filter impulse response. 2. Find the output of the filter when the input x[n] using linear convolution. 3. Find the filter frequency response using a. MATLAB (freqz) and b. MATLAB (FFT). 4. What was the effect of the filter on the signal? Explain! 5. Is the frequency response of the filter consistent with the result obtained in part 2? Explain. 6. Find the filter frequency response by hand. Is this result consistent with the one obtained in part 3? 7. What type of a filter is this one (LP, BP, or HP). 8. Repeat all parts from 1 to 7 for the following causal FIR filter y[n] = 0.5 x[n] -0.5 x[n-1] Given the following signal x[n]= [20 18 22 17 23 19 21 17 18 14 16 12 14 11 12 9 10 7 8 4 7 ] and a causal FIR filter characterized by the following difference equation: y[n] = 0.5 x[n] + 0.5 x[n-1] Ikhlas Abdel-Qader Page 1 of 1 5/14/2020

Problem 1 Write MATLAB Program to compute and plot the frequency response of a causal LTI discrete-time system with a transfer function given by for 0     . What type of filter does it represent? H(z)  0.15(1 z2 ) 10.5z1 0.7z2 Problem 2 Repeat Problem 2 for the following transfer function: … Continue reading Problem 1 Write MATLAB Program to compute and plot the frequency response of a causal LTI discrete-time system with a transfer function given by for 0     . What type of filter does it represent? H(z)  0.15(1 z2 ) 10.5z1 0.7z2 Problem 2 Repeat Problem 2 for the following transfer function: H(z)  0.15(1 z2 ) 0.70.5z1 z2 What is the difference between the two filters in problem 1 and problem2, respectively? Which one will you choose for filtering and why? Problem 3 1. Find this filter impulse response. 2. Find the output of the filter when the input x[n] using linear convolution. 3. Find the filter frequency response using a. MATLAB (freqz) and b. MATLAB (FFT). 4. What was the effect of the filter on the signal? Explain! 5. Is the frequency response of the filter consistent with the result obtained in part 2? Explain. 6. Find the filter frequency response by hand. Is this result consistent with the one obtained in part 3? 7. What type of a filter is this one (LP, BP, or HP). 8. Repeat all parts from 1 to 7 for the following causal FIR filter y[n] = 0.5 x[n] -0.5 x[n-1] Given the following signal x[n]= [20 18 22 17 23 19 21 17 18 14 16 12 14 11 12 9 10 7 8 4 7 ] and a causal FIR filter characterized by the following difference equation: y[n] = 0.5 x[n] + 0.5 x[n-1] Ikhlas Abdel-Qader Page 1 of 1 5/14/2020