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 } }

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# The joint probability density function of X and Y is given by f(x,y)=67(x2+xy2)0

# Find the magnetic field intensity (π»”β) for all points in the space for the given current distribution. I, πΌ, π½’,π, πππ πΎ πππ ππππ π‘ππ‘ππ‘π . Note that there is no current for π > π b) Find the magmetic field intensity for just before and after π = π πππ π = π (need to do on β an d + of b and c) c) Examine magentic boundary conditions at π = π πππ π = π For this part you need to set up “”””β “”””β 9π»: β π»<=π₯π? πππππ‘πππ¦ π? π€hππ‘ ππ πππ π hππ€ ππ π‘hπ πππ’πππππ¦ ππππππ‘πππ π€ππππ π‘π πππ‘ ππ’ππ πππππ‘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· ο£ ο° . What type of filter does it represent? H(z) ο½ 0.15(1ο zο2 ) 1ο0.5zο1 ο«0.7zο2 Problem 2 Repeat Problem 2 for the following transfer function: H(z) ο½ 0.15(1ο zο2 ) 0.7ο0.5zο1 ο«zο2 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 z2 ) 10.5z1 0.7z2 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 z2 ) 10.5z1 0.7z2 Problem 2 Repeat Problem 2 for the following transfer function: H(z) 0.15(1 z2 ) 0.70.5z1 z2 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

# 1. A conducting bar is put in a constant magnetic field B = 0.1T. The circuit resistance is R =10Ξ©. The bar width is 20cm. The mass of the bar is m = 1kg. The circuit and the metal bar are on a flat horizontal surface. If the bar has an initial speed (t = 0) of V0 = 4m/s, determine: (a) The current generated in the bar at t = 0; (b) The force experienced by the conducting bar at t = 0; (c) The speed of the bar at time t = 10s;

# Using the Laplace transform application find i(t) t>0

# A parallel resonant band pass filter has a resistance of 5k and cutoff frequency of 9875 rad/s and 10125 rad/s the circuit has a high Q determine

A parallel resonant band pass filter has a resistance of 5k and cutoff frequency of 9875 rad/s and 10125 rad/s the circuit has a high Q determine the bandwidth B the resonant frequency t he quality factor Q the capacitance the inductance