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12. (a) Show that ifXandy are independent, then EC-P) = Eal) and X = sin Θ,...
Let Θ be a continuous random variable uniformly distributed on [0,2 Let X = cose and Y sin e. Sho...
Let Θ be a continuous random variable uniformly distributed on [0,2 Let X = cose and Y sin e. Show that, for this X and Y, X and Y are uncorrelated but not independent. (Hint: As part of the solution, you will need to find E[X], E[Y] and E|XY]. This should be pretty easy; if you find yourself trying to find fx(x) or fy (v), you are doing this the (very) hard way.)
Let Θ be a continuous random variable...
Let Θ be a continuous random variable uniformly distributed on [0,2 Let X = cose and...
Let Θ be a continuous random variable uniformly distributed on [0,2 Let X = cose and Y sin e. Show that, for this X and Y, X and Y are uncorrelated but not independent. (Hint: As part of the solution, you will need to find E[X], E[Y] and E|XY]. This should be pretty easy; if you find yourself trying to find fx(x) or fy (v), you are doing this the (very) hard way.)
Consider a point P on the x − y plane. Show that ur = cos(θ) ˆi...
Consider a point P on the x − y plane. Show that ur = cos(θ) ˆi
+ sin(θ) ˆj, uθ = − sin(θ) ˆi + cos(θ) ˆj.
Q5) Relationship between the Polar and Cartesian Unit Axis Vec- tors] Consider a point P on the x - y plane. Show that u.-cos(0)İ + sin(θ)j. u.--sin(θ)i + oos@j
11. Short proofs (a) Show that if the rvs Y and Yare independent, they are uncorrelated....
11. Short proofs (a) Show that if the rvs Y and Yare independent, they are uncorrelated. (b) Let X and Y be uncorrelated random variables with non-zero means. Can X and Ybe orthogonal? (c) Let X, Y and Z be random variables such that (i) Are X and y orthogonal? (Show why or why not.) (ii) Are X and y correlated? (Show why or why not.)
Consider the following surface parametrization. x-5 cos(8) sin(φ), y-3 sin(θ) sin(p), z-cos(p) Find an expression for a unit vector, n, normal to the surface at the image of a point (u, v) for θ in [...
Consider the following surface parametrization. x-5 cos(8) sin(φ), y-3 sin(θ) sin(p), z-cos(p) Find an expression for a unit vector, n, normal to the surface at the image of a point (u, v) for θ in [0, 2T] and φ in [0, π] -3 cos(θ) sin(φ), 5 sin(θ) sin(φ),-15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 3 cos(9) sin(9),-5 sin(θ) sin(9), 15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 v 16 sin2(0) sin2@c 216 cos2@t9(3 cos(θ) sin(φ), 5 sin(θ) sin(φ) , 15 cos(q) 216 cos(φ)...
help please!! Evaluate the integral using the two different methods given. S sin 0 cos do,...
help please!!
Evaluate the integral using the two different methods given. S sin 0 cos do, A. Use Substitution Rule with u = sin(0) B. Use Identity: sin(20) = 2 sin 0 cos 0. Show all work on your paper. Label each answer with the part (A or B). Let y = f(x) be a continuous function. f(-2) = -4, f(1) = 0, and f(3) = -2 Domain of Y is (-0,00). For all æ in (-0, 1) U (3,...
Let X ~ POI(μ), and let θ-P(X = 0-e-". (a) Is -e-r an unbiased estimator of θ? (b) Show that θ = ...
this is a challenging question
Let X ~ POI(μ), and let θ-P(X = 0-e-". (a) Is -e-r an unbiased estimator of θ? (b) Show that θ = u(X) is an unbiased estimator of θ, where u(0) 1 and u(x)-0 if (c) Compare the MSEs of, and è for estimating θ-e-, when μ 1 and 2.
Let X ~ POI(μ), and let θ-P(X = 0-e-". (a) Is -e-r an unbiased estimator of θ? (b) Show that θ = u(X) is an...
. (a) Show that the function u= 4x2 - 12.xy2 is harmonic and v=12.xy-4v2 is a...
. (a) Show that the function u= 4x2 - 12.xy2 is harmonic and v=12.xy-4v2 is a harmonic conjugate of u. [Consequently, the function f =u+iv is entire, thus it has an antiderivative and that any contour integral of f is path independent.] (b) Find an antiderivative F(-)= F(x+iy)=P(x, y)+i Q(x, y) of the function f; and (c) evaluate ( f (2) ds , where C is any contour from 0 to 1–2i .
4. Let X have the following PDF: sin(x) , 0 < x < π , otherwise...
4. Let X have the following PDF: sin(x) , 0 < x < π , otherwise Ix(x) = 0 Find the CDF of X Using the Probability Integral Transformation Theorem, describe the process of generating values from the density of X Using R, generate 1,000 values using your process in part b. Produce a histogram of these generated values, and overlay the density curve of X over top. (Hint: in R, the function acos calculates the inverse cosine function.) Using...
X and Y are random variables (a) Show that E(X)=E(B(X|Y)). (b) If P((X x, Y )...
X and Y are random variables (a) Show that E(X)=E(B(X|Y)). (b) If P((X x, Y ) P((X x})P({Y y)) then show that E(XY) = E(X)E(Y), i.e. if two random variables are independent, then show that they are uncorrelated. Is the reverse true? Prove or disprove (c) The moment generating function of a random variable Z is defined as ΨΖφ : Eez) Now if X and Y are independent random variables then show that Also, if ΨΧ(t)-(λ- (d) Show the conditional...
Let Θ be a continuous random variable uniformly distributed on [0,2 Let X = cose and Y sin e. Show that, for this X and Y, X and Y are uncorrelated but not independent. (Hint: As part of the solution, you will need to find E[X], E[Y] and E|XY]. This should be pretty easy; if you find yourself trying to find fx(x) or fy (v), you are doing this the (very) hard way.)
Let Θ be a continuous random variable...
Let Θ be a continuous random variable uniformly distributed on [0,2 Let X = cose and Y sin e. Show that, for this X and Y, X and Y are uncorrelated but not independent. (Hint: As part of the solution, you will need to find E[X], E[Y] and E|XY]. This should be pretty easy; if you find yourself trying to find fx(x) or fy (v), you are doing this the (very) hard way.)
Consider a point P on the x − y plane. Show that ur = cos(θ) ˆi
+ sin(θ) ˆj, uθ = − sin(θ) ˆi + cos(θ) ˆj.
Q5) Relationship between the Polar and Cartesian Unit Axis Vec- tors] Consider a point P on the x - y plane. Show that u.-cos(0)İ + sin(θ)j. u.--sin(θ)i + oos@j
11. Short proofs (a) Show that if the rvs Y and Yare independent, they are uncorrelated. (b) Let X and Y be uncorrelated random variables with non-zero means. Can X and Ybe orthogonal? (c) Let X, Y and Z be random variables such that (i) Are X and y orthogonal? (Show why or why not.) (ii) Are X and y correlated? (Show why or why not.)
Consider the following surface parametrization. x-5 cos(8) sin(φ), y-3 sin(θ) sin(p), z-cos(p) Find an expression for a unit vector, n, normal to the surface at the image of a point (u, v) for θ in [0, 2T] and φ in [0, π] -3 cos(θ) sin(φ), 5 sin(θ) sin(φ),-15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 3 cos(9) sin(9),-5 sin(θ) sin(9), 15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 v 16 sin2(0) sin2@c 216 cos2@t9(3 cos(θ) sin(φ), 5 sin(θ) sin(φ) , 15 cos(q) 216 cos(φ)...
help please!!
Evaluate the integral using the two different methods given. S sin 0 cos do, A. Use Substitution Rule with u = sin(0) B. Use Identity: sin(20) = 2 sin 0 cos 0. Show all work on your paper. Label each answer with the part (A or B). Let y = f(x) be a continuous function. f(-2) = -4, f(1) = 0, and f(3) = -2 Domain of Y is (-0,00). For all æ in (-0, 1) U (3,...
this is a challenging question
Let X ~ POI(μ), and let θ-P(X = 0-e-". (a) Is -e-r an unbiased estimator of θ? (b) Show that θ = u(X) is an unbiased estimator of θ, where u(0) 1 and u(x)-0 if (c) Compare the MSEs of, and è for estimating θ-e-, when μ 1 and 2.
Let X ~ POI(μ), and let θ-P(X = 0-e-". (a) Is -e-r an unbiased estimator of θ? (b) Show that θ = u(X) is an...
. (a) Show that the function u= 4x2 - 12.xy2 is harmonic and v=12.xy-4v2 is a harmonic conjugate of u. [Consequently, the function f =u+iv is entire, thus it has an antiderivative and that any contour integral of f is path independent.] (b) Find an antiderivative F(-)= F(x+iy)=P(x, y)+i Q(x, y) of the function f; and (c) evaluate ( f (2) ds , where C is any contour from 0 to 1–2i .
4. Let X have the following PDF: sin(x) , 0 < x < π , otherwise Ix(x) = 0 Find the CDF of X Using the Probability Integral Transformation Theorem, describe the process of generating values from the density of X Using R, generate 1,000 values using your process in part b. Produce a histogram of these generated values, and overlay the density curve of X over top. (Hint: in R, the function acos calculates the inverse cosine function.) Using...
X and Y are random variables (a) Show that E(X)=E(B(X|Y)). (b) If P((X x, Y ) P((X x})P({Y y)) then show that E(XY) = E(X)E(Y), i.e. if two random variables are independent, then show that they are uncorrelated. Is the reverse true? Prove or disprove (c) The moment generating function of a random variable Z is defined as ΨΖφ : Eez) Now if X and Y are independent random variables then show that Also, if ΨΧ(t)-(λ- (d) Show the conditional...
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