Answered: Statistic question for signals please… | bartleby

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 62CR

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Solve 2

Statistic question for signals please help.
Let Z(t)=X(t)+Y(t), where X(t) and Y(t) are
independent random signals. Derive the
formulas for:
i) μz (t).
ii) Rz (t, t+T)

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b) Let Z₁-N(0,1), and W₁ = Y~N(0,1), for i=1,2,3,...,10, then: dx dy i) State, with parameter(s), the probability distribution of the statistic, T = - 154 ii) Find the mean and variance of the statistic T = ₁² 10 iii) Calculate the probability that a statistic T = Z₁ + W₁ is at most 4. iv) Find the value of ß such that P(T> B) = 0.01, where T = ₁2₁² +².
Two random variables X andY are related by the expression Y = aX +b, where ta' and 'b' are any real numbers.
ExeR. 2. PrOve That opTimaL Variance V = と」 Di bouND Saris Fies THe uppeR V < min Ai
Suppose that Y₁ and Y₂ are uniformly distributed over the triangle shaded in the accompanying figure. 3₂ (0, 1) (-1,0) (a) Find Cov(Y₁ Y₂). Cov(Y₁, Y₂) = (b) Are Y₁ and Y₂ independent? Yes O No (1, 0) (c) Find the coefficient of correlation for Y₁ and Y₂. P= y/₁ (d) Does your answer to part (b) lead you to doubt your answer to part (a)? Why or why not? O Even though Cov(Y₁Y₂) # 0, Y₁ and Y₂ are not necessarily dependent. Since Cov(Y₁ Y₂) # 0, we should expect Y₁ and Y₂ to be dependent. O Since Cov(Y₁, Y₂) = 0, we should expect Y₁ and Y₂ to be independent. O Even though Cov(Y₁Y₂) = 0, Y₁ and Y₂ are not necessarily independent.
A dart player throws a dart at a target whose centre is located at the point (0, 0). The dart lands at the point (x, y), where x is an observation on a G(0, 1) random variable, X, and y is an observation on a G(0, 1) random variable, Y. The random variables X and Y are independent. If the dart lands inside the unit circle (i.e. circle with radius 1) centred at (0, 0), the player wins a prize. What is the probability that the dart thrower wins a prize? Hints: The distance formula along with the x2 or Exponential distributions will be helpful to solve this question. You may also use R to solve for this probability. A) 0.843 B) 0.683 C) 0.466 D) 0.393
Value of Y 14 22 30 40 65 0.02 0.05 0.10 0.03 0.01 Value of X 5 0.17 0.15 0.05 0.02 0.01 8 0.02 0.03 0.15 0.10 0.09
b) Let Z₁ = X-X~N(0,1), and W₁ i) State, with parameter(s), the probability distribution of the statistic, T = ox YHY~N(0,1), for i=1,2,3,...,10, then: oy 10 ii) Find the mean and variance of the statistic T = ² 1,²₁² Σt=12₁ SiaWi iii) Calculate the probability that a statistic T = Z₁ + W₁ is at most 4. iv) Find the value of ß such that P(T> B) = 0.01, where T = Σ₁Z₁²+₁Wi².
Q/Fit (y = ax² + (b/x)) to the following data: (x:1, 2, 3, 4), (y: -1.51, 0.99, 3.88, 7.66). *
What is the orthogonality assumption in OLS, taking Y = a + bX as the model, and the error term is e? (e is epsilon) Correlation(X, X) = 0 O Correlation(X, e) = 0 O Correlation(e, X)= 1 None of the above
ele) Consider the regression model Y; = BX; + u; Where u, and X, satisfy the assumptions specified here. Let p denote an estimator of p that is constructed as ß= where Y and X are the sample means of Y, and X, respectively. Show that B is a linear function of Y,, Y2, Y Show that B is conditionally unbiased. 1 E(Y,X,, X2.. X,) = ▼ 1 „P(X, +X2+ + X,) + Y2 + + Yn) (AX, + u) 2 E(BIX,. X2 X,) =E |(X, X2.. Xn) Click to select your answer(s). W DELL P Type here to search 1/5
Let X and Y be random variables, and a and b be constants. ???? a) Show that Cov [aX,bY] = abCov [X,Y] . b) Show that if a > 0 and b > 0, then the correlation coefficient between aX and bY is the same as the correlation coefficient between X and Y . c) Is the correlation coefficient between X and Y unaffected by changes in the units of X and Y ?

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