Let a,b,c and d be constants. Use the rules of expected value to show that Cov(aX+b, cY+d) = ac Cov(X,Y).

Q: Prove that Cov (x, y) = E (xy) – E (x) E (y).

A: Cov(x,y) is covariance of x and y. E(x) is expected value of x E(y) is expected value of y.

Q: Let X and Y denote be as follows: E(X) = 10, E(X2) = 125, E(Y) = 20, Var(Y) =100 , and Var(X+Y) =…

A: Given data E(X) = 10, E(X2) = 125, E(Y) = 20, Var(Y) =100 , and Var(X+Y) = 155.  W = 2X-Y and  T =…

Q: 3. Determine a and b for Y X1 and Y2aX bX2 such that EX1 EX2}= 0, Var(X) Var(X2) Var(Yi) Var(2) 1,…

A: The provided information is:

Q: Suppose we have the quadratic function f(x)=A(x^2)+C where the random variables A and C have…

A: A quadratic equation is written as f(x)=Ax2+Bx+C. f(x) has real roots if B2-4AC≥0.

Q: Show that (A − B )T = AT − B T .

A: Given  (A − B )T = AT − B T

Q: A dice is rolled twice. Let X equal the sum of the outcomes, and let Y equal the first outcome minus…

A: In probability theory and statistics, covariance measures how two random variables are jointly…

Q: X and Y have the following joint distribution: 2 1 2c Y 2 c/2 Find COV(X,Y). A) – B) - C) 0 D) E) {…

A: Given Data     x   y   1 2 Total 1 c 2c 3c 2 c/2 c 3c/2…

Q: (i) Find the conditional pdf's fyx2 and X y

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Q: Complete the proof that AUVX ATWX. U V T. W

A: Given:  WX=VX and UX=TX. In △UVX and △TWX WX=VX                  (Given) UX=TX…

Q: Let Xn ☆ Bil^,p] where n& P ae wnknown. Find method of moments estimators for n&

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Q: Q3: show that: S yi va -y dy =na² where a is a positive constatnt

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Q: jn= 16, α=0.05

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Q: Show that: (a) Cov(X,Y) = E[XY] – E[X]E[Y]. (b) If X and Y are independent, then fY|X(y|x) = fY(y)

A: Solution:a.Show that COV(X,Y)=E(XY)–E(X)E(Y)

Q: The DE : y' = e5x-7y is seperable Select one: True False

A:

Q: Let & be a minimax estimator of 0 under the squared error loss. Show that co+ c1o is a minimax…

A: Given that: δ be a minimax estimator of θ under the squared error loss. sinx+1=0sinx=-1…

Q: Assume random vector y has E(y) = μ RP and Cov(y) = Σ > 0. (a) Find E[(y-μ)'(y -μ)]. (b) Show that…

A: Random vector         A random vector value depends on the outcome of the experiment. A random…

Q: The joint pmf of X and Y is f(x, y) = 1/6, 0 ≤ x+y ≤ 2, where x and y are nonnegative integers.…

A: Joint pdf of X & Y is        f(x,y)=1/6;  0≤x+y≤2, x,y>00  ; elsewhere Marginal pdf of X is…

Q: Find the covariance between x and y

A:

Q: Q2: Find the total energy of the signal: fcos*(«) -sts π (x) Sts. x(t) : 0.w. (-R2, 0) (x2,0)

A: We will integrate the function in the given range.

Q: Use the Chain Rule to find az/əs and ôz/Ət. z = tan(u/v), u = 8s + 3t, V = 3s – 8t

A: z=tanuv,   u=8s+3t,   v=3s−8tFormula→∂z∂t=∂z∂u⋅∂u∂t+∂z∂v⋅∂v∂t

Q: A nermally distolated cndee erióbh with medn e has ė pabiblity dansty pabibiliy Ancty fnctin fris by

A: The normal distribution: A continuous random variable X is said to follow normal distribution if the…

Q: Calculate the covariance and correlation between X and Y. dint: Use the computational formula to…

A: Solution: The joint PMF of (X, Y)   value of Y    14 22 30 40 65 Total  Value of X 1 0.02…

Q: s show that: sinhCA+B) = SinhA. cush B + Cosh A. simhB

A:

Q: Integrate: Show that B(p+1,q)+B(p,q+1)=B(p,q).

A:

Q: Suppose that the j.p.d.f.,f(x,y) = {(x² + y), 0<x<1,0 <y<1 zero elsewhere. Find: a- The joint c.d.f.…

A: Let X and Y have jont pdf f(x,y)=(6/5)*(x2+y) ,0&lt;x, y &lt;1 a) Joint  cdf of X and Y…

Q: al HL b7 SAS C) NOt Co ng ruent

A: We will prove what relationship these two triangles have.

Q: find an antiderivative Fon of the function fox)=5sinX such that FCO)=1.

A:

Q: Let S be a randor mpute E(S|Z).

A: Here S be a random variable with P(S&gt;t)=e-t where t&gt;0 let Z=min(s,t) hence P(S&lt;t)=1-e-t…

Q: Find the covariance of Y,, Y, and Cyy.

A:

Q: Find e² in the form of u + jv and le²| for z = 2 + 3nj

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Q: Compute the z-value if u = 140, o = 14, x = 145 and n = 12. Assume that the population is normally…

A:

Q: Let X ~ Uniform(-1,1) and Y = X² , find the CDF and PDF.

A: Use the following definitions, to obtain the solution. The cumulative distribution function of a…

Q: Let X be a random vuniable with PAF FlnS= %3D otherwise s Find the constunt c J Find ECH and Vor (xS

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Q: Evaluate Sm e" dæ. • 2 does not exist (diverges)

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Q: LZHP - DTNV. Complete the statement below. ZZ = _2_

A: Consider the following condition: LZHP~DTNV Hence, ∠L≅∠D∠Z≅∠T∠H≅∠N∠P≅∠V

Q: (z In z + 5)dz

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Q: let the jonit Pid f. for the random varables X.y given by flx.yj-3x- 8xy+6j,04x<1 ,o2Yel find…

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Q: What is (are) the most probable position(s) for a particle confined to a box with 0 < x < a and n =…

A: It is given that A particle confined to a box with 0&lt;x&lt;a and n=3

Q: Let E(X|Y = y) = 3y and var(X|Y = y) = 2, and let Y have the p. d. f. %3D %3D if y > 0 e-y fG) = lo…

A: Given EXY=y=3y      and   varXY=y=2 Y have the p.d.f       fy=e-y        if   y&gt;0 0…

Q: Use the chain rule and compute if z = x2 + xy, x = uv? + w°y = u + ve"

A: z=x2+xy3, x=uv2+w3, y=u+vew

Q: Show that S ťe dt = 3VI

A:

Q: Find the measures of ZX and ZY.

A: we need first the sum of interior angles for a pentagon this is given by the formula,      (n-2) ×…

Q: Example Find the F.T of rectangular pulse To - f(t) = A rec T

A: Given query is to find the Fourier Transformation of the expression.

Q: Evaluate xy dS. S: z = 3 – x – y, first octant

A: Given query is to find the double integral in first octane.

Q: Prove that (A')' = A for each A E Mmxn(F).

A: