a lal a. 01 : R³ → → M22(R) given by 0 where |2| is the modulus of x.

Q: Oz Aradom Variable(x) has the following cof FX(X) = (x³ + x) al find the pdf of X find Pro <xcot)…

A: Given that: The cdf of random variable X is given as: FxX=12X3+X      where 0≤X≤1

Q: Let X Gamma(a, B). Prove that for any positive integer n > 1, E(X") = [(a +n– 1)(a+n – 2)..-a]3".

A: It is given in the question that X~Gammaα,β then we have to prove that for any positive integer n≥1.…

Q: Let the moment generating function of Z be mZ(t) = 1/(1−4t)2, t∈(−0.25,0.25). Solve for the…

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Q: A circular shaft has a diameter d [m] that varies with axial position x [m] according to d =…

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Q: Example f:[-l,l>iR Such Hhet f is continuons, But has unbounded Elsi] 3 pr Give an (3) Variatien on

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Q: Let X represent the outcome when a balanced die is tossed. If g(X) = 3X²+4, Find: a) Ag(X) 2 b)…

A: Given that: X represents the outcome when balanced die is tossed g(X)=3X2+4

Q: Determine | An (x) An+1(x) dx, from the relation: tn .1 Σ (2n + 1)! tn+1 A, (x) An+1(x) dx n=0 n -1

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Q: Prove that m-l dx =0 m +n (し+x)" where m,n are both Positive

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Q: b) Suppose that f is the Expon(5) PDF. Compute SLf(x) dx.

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Q: Pro ve 8さt(.)る %3D (Srh)(らtM ー7 \et: ヒこe

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Q: Find the moment generating function of x - f(x) = 1, where 0 < x < 1 Select one: а. et 1 t b. 1 (e'…

A: Let X be a continuous random variable with probability density function f(x). Then the moment…

Q: Suppose that fex, & C² [0, 1], fixo Lo at f fox dx fill L 0 Prove that

A: What is Antiderivative: In calculus, a differentiable function F whose derivative is identical to…

Q: dt Use parseval's identity to prove that J a? +6²+?) 2ab (a + b) TC

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Q: (a) Prove that Σ³ = n²(n+1) ². j=1 (b) Evaluate fr³ de directly from the definition, without using…

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Q: Determine k, so that ƒx,y(x, y) (x,y) =. a) Determine fylx=.25(0.5) b) Determine E[X] c) Determine…

A: Given: The joint pdf is given fx,yx,y=kx0&lt;x&lt;y&lt;10otherwise

Q: The joint PDF of the r.v. A and B is constant on (a, b): a, b > 0n 0.5 0.5|X<0.5).

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Q: Let X- N(10, 5'). What is P(X > 3)?

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Q: urier Series for the periodic signal f(t) = t (0 ≤t≤2m).

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Q: e that M{(1 + xa)-b; p} = %3D

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Q: Determine DFT X[ej"] of the signal (answer a or b) a) x[n]coswon. b) x(n) = a"u(-n- 1) %3D

A: As it's mentioned in the question to answer between a) or b), so showing steps for only one part. b)…

Q: O from the equation z = In(x² + y²) + Zyy Show that zxx %3D

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Q: 3.Find the Fourier series of the function www www ww f(x)= f(x)=x f(x)=Tt

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Q: Let U = N, A = {1, 3, 5}, B = {x : x² - 6x + 5 = 0}, and D = {x :x > 5}. Find h. D'n (AUB)

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Q: Let n be an even integer. Prove that Dn/Z(Dn) is isomorphic to Dn/2.

A: Given that 'n' be an even integer.  To prove that DnZDn is isomorphic to Dn2.

Q: a Find the Orthogonal trajectories of the family of r =; 1+coso

A: we need to find the orthogonal trajectories of the given family of the curve in the polar form.

Q: Let X, and X, independence r.v. have same moment generating functi (1-) where where tsa, let Y=aX,…

A: Given: MX1t=MX2t=1-tα-1Y=aX1+bX2

Q: make the ODE's inot variabke separable using a substitution. dy/dx=((1-2x-5y)^1/2 )/((2x+5y)^1/3

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Q: Consider the pdf 1/3(z) 0<I<∞ fz(x) = {3 elsewhere. Find the cdf of X.

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Q: 3.) Find the DFT of f = [1 -2 1 2]!

A: Sol