EBK MATLAB: AN INTRODUCTION WITH APPLIC
5th Edition
ISBN: 8220102007642
Author: GILAT
Publisher: YUZU
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Chapter 5, Problem 2P
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a. Find the value of A.b. Find pX(x) and py(y).c. Find pX|y(x|y) and py|X(y|x)d. Are x and y independent? Why or why not?
The PDF of an amplitude X of a Gaussian signal x(t) is given by:
The PDF of a random variable X is given by the equation in the picture.
Chapter 5 Solutions
EBK MATLAB: AN INTRODUCTION WITH APPLIC
Ch. 5 - Prob. 1PCh. 5 - Plot the function fx=3cosxsinxe0.2x for 4x9 .Ch. 5 - Plot the function fx=x22+sinx+x4 for 4x4 .Ch. 5 - Plot the function fx=x32x210sin2xe0.9x and its...Ch. 5 - Make two separate plots of the function...Ch. 5 - Use the fplot command to plot the function...Ch. 5 - Plot the function fx=sin2xcos2x ad its derivative,...Ch. 5 - Make a plot of a circle with its center at (4.2,...Ch. 5 - A parametric equation is given by...Ch. 5 - Two parametric equation are given by:...
Ch. 5 - Plot the function fx=x25x12x2x6 in the domain 1x7...Ch. 5 - Prob. 12PCh. 5 - Prob. 13PCh. 5 - An epicycloid is a curve (shown partly in the...Ch. 5 - The shape of the pretzel shown is given by...Ch. 5 - Prob. 16PCh. 5 - Plot an ellipse with major axes of a = 10 and b =...Ch. 5 - The following data gives the approximate...Ch. 5 - The force F (in N) acting between a particle with...Ch. 5 - Prob. 20PCh. 5 - Consider the motion of the squirrel in the...Ch. 5 - The curvilinear motion of a particle is defined by...Ch. 5 - The demand for water during a fire is often the...Ch. 5 - The position x as a function of time of a particle...Ch. 5 - The area of the aortic valve, AVin cm2, can be...Ch. 5 - A bandpass filter passes signals with frequencies...Ch. 5 - A resistor, R = 4O, and an inductor, L = 1.3 H,...Ch. 5 - In a typical tension test a dog bone shaped...Ch. 5 - According to special relativity, a rod of length L...Ch. 5 - The shape of a symmetrical four-digit NACA airfoil...Ch. 5 - The ideal gas law relates the pressure P, volume...Ch. 5 - The be vibrations of the body of a helicopter due...Ch. 5 - A railroad bumper is designed to slow down a...Ch. 5 - Consider the diode circuit shown in the figure....Ch. 5 - Prob. 35PCh. 5 - A simply supported beam is subjected to...Ch. 5 - Biological oxygen demand (BOD) is a measure of the...Ch. 5 - The temperature dependence of the diffusion...Ch. 5 - The resonant frequency f (in Hz) for the circuit...Ch. 5 - The Taylor series for cos(x) is:...
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- For a binary asymmetric channel with Py|X(0|1) = 0.1 and Py|X(1|0) = 0.2; PX(0) = 0.4 isthe probability of a bit of “0” being transmitted. X is the transmitted digit, and Y is the received digit.a. Find the values of Py(0) and Py(1).b. What is the probability that only 0s will be received for a sequence of 10 digits transmitted?c. What is the probability that 8 1s and 2 0s will be received for the same sequence of 10 digits?d. What is the probability that at least 5 0s will be received for the same sequence of 10 digits?arrow_forwardV2 360 Step down + I₁ = I2 10KVA 120V 10KVA 1₂ = 360-120 or 2nd Ratio's V₂ m 120 Ratio= 360 √2 H I2 I, + I2 120arrow_forwardQ2. [20 points] An amplitude X of a Gaussian signal x(t) has a mean value of 2 and an RMS value of √(10), i.e. square root of 10. Determine the PDF of x(t).arrow_forward
- In a network with 12 links, one of the links has failed. The failed link is randomlylocated. An electrical engineer tests the links one by one until the failed link is found.a. What is the probability that the engineer will find the failed link in the first test?b. What is the probability that the engineer will find the failed link in five tests?Note: You should assume that for Part b, the five tests are done consecutively.arrow_forwardProblem 3. Pricing a multi-stock option the Margrabe formula The purpose of this problem is to price a swap option in a 2-stock model, similarly as what we did in the example in the lectures. We consider a two-dimensional Brownian motion given by W₁ = (W(¹), W(2)) on a probability space (Q, F,P). Two stock prices are modeled by the following equations: dX = dY₁ = X₁ (rdt+ rdt+0₁dW!) (²)), Y₁ (rdt+dW+0zdW!"), with Xo xo and Yo =yo. This corresponds to the multi-stock model studied in class, but with notation (X+, Y₁) instead of (S(1), S(2)). Given the model above, the measure P is already the risk-neutral measure (Both stocks have rate of return r). We write σ = 0₁+0%. We consider a swap option, which gives you the right, at time T, to exchange one share of X for one share of Y. That is, the option has payoff F=(Yr-XT). (a) We first assume that r = 0 (for questions (a)-(f)). Write an explicit expression for the process Xt. Reminder before proceeding to question (b): Girsanov's theorem…arrow_forwardProblem 1. Multi-stock model We consider a 2-stock model similar to the one studied in class. Namely, we consider = S(1) S(2) = S(¹) exp (σ1B(1) + (M1 - 0/1 ) S(²) exp (02B(2) + (H₂- M2 where (B(¹) ) +20 and (B(2) ) +≥o are two Brownian motions, with t≥0 Cov (B(¹), B(2)) = p min{t, s}. " The purpose of this problem is to prove that there indeed exists a 2-dimensional Brownian motion (W+)+20 (W(1), W(2))+20 such that = S(1) S(2) = = S(¹) exp (011W(¹) + (μ₁ - 01/1) t) 롱) S(²) exp (021W (1) + 022W(2) + (112 - 03/01/12) t). where σ11, 21, 22 are constants to be determined (as functions of σ1, σ2, p). Hint: The constants will follow the formulas developed in the lectures. (a) To show existence of (Ŵ+), first write the expression for both W. (¹) and W (2) functions of (B(1), B(²)). as (b) Using the formulas obtained in (a), show that the process (WA) is actually a 2- dimensional standard Brownian motion (i.e. show that each component is normal, with mean 0, variance t, and that their…arrow_forward
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- I just need to know why this is wrong below: What is the test statistic W? W=5 (incorrect) and What is the p-value of this test? (p-value < 0.001-- incorrect) Use the Wilcoxon signed rank test to test the hypothesis that the median number of pages in the statistics books in the library from which the sample was taken is 400. A sample of 12 statistics books have the following numbers of pages pages 127 217 486 132 397 297 396 327 292 256 358 272 What is the sum of the negative ranks (W-)? 75 What is the sum of the positive ranks (W+)? 5What type of test is this? two tailedWhat is the test statistic W? 5 These are the critical values for a 1-tailed Wilcoxon Signed Rank test for n=12 Alpha Level 0.001 0.005 0.01 0.025 0.05 0.1 0.2 Critical Value 75 70 68 64 60 56 50 What is the p-value for this test? p-value < 0.001arrow_forwardons 12. A sociologist hypothesizes that the crime rate is higher in areas with higher poverty rate and lower median income. She col- lects data on the crime rate (crimes per 100,000 residents), the poverty rate (in %), and the median income (in $1,000s) from 41 New England cities. A portion of the regression results is shown in the following table. Standard Coefficients error t stat p-value Intercept -301.62 549.71 -0.55 0.5864 Poverty 53.16 14.22 3.74 0.0006 Income 4.95 8.26 0.60 0.5526 a. b. Are the signs as expected on the slope coefficients? Predict the crime rate in an area with a poverty rate of 20% and a median income of $50,000. 3. Using data from 50 workarrow_forward2. The owner of several used-car dealerships believes that the selling price of a used car can best be predicted using the car's age. He uses data on the recent selling price (in $) and age of 20 used sedans to estimate Price = Po + B₁Age + ε. A portion of the regression results is shown in the accompanying table. Standard Coefficients Intercept 21187.94 Error 733.42 t Stat p-value 28.89 1.56E-16 Age -1208.25 128.95 -9.37 2.41E-08 a. What is the estimate for B₁? Interpret this value. b. What is the sample regression equation? C. Predict the selling price of a 5-year-old sedan.arrow_forward
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