es A1, A2,..., An have a common nonzero fr 2, and the correlation between any pair of r d hence prove that -1/(n-1) ≤p≤ 1. Q = o[X² + b (x₁) i=1 estimate of o2, find a and b. Hence show t Q n Σ i=1 2 (X₂ - X)² (1-p)(n-1)'

Q: %3D Using the substitution u= 2, find the values of x such that 22r+2 = 5 (2)-

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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: Starting from the function f(x) = e¬alx| -L 1 where

A:

Q: 3. Consider the impulse response function h[n] and input signal x[n]given as; h[n] = [1-130 2] x[n]…

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Q: Apply Parseval's identity to the function f (x) = x, - nSxSn and deduce that n16 = 1/12+1/22 + . +…

A: For the solution follow the next steps.

Q: Exercise 4: How many functions f exist such that f'(x) = 3x2 - 6r +3, and (1,-2) is a point of…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 5. For the signal below find the following manipulations in time x(1) 12 а. [x (2t - 3)] b. x(1 –…

A: The solution is given below in the next step:

Q: Let fn(x) = 1+cos2 2023 (na). Does {f} converge uniformly to a function f on R? √n

A:

Q: Let X and Y be statistically independent random variables with Var(X) = 4 and Var(Y) = 10. We do not…

A: The provided information is as follows:. and  are independent random variables..

Q: Draw the auto-correlation function d(t) = [rect () – tri ()1 4

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Q: Let X, and X, independence r.v. have same moment generating function (1-) where isa, let Y=aX₁…

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Q: 1 If z = 2 V3 -i, then find ()*

A: Given complex number is: z=-1-3i2 Find the conjugate of complex number: z¯=-1+3i2 Find z¯4?

Q: 1. We can generalize our approach to warto for any state function. Consider: f = 3x²³ - 2xy² for X₂…

A: As per the question, we will verify the above for f=3x3-2xy2. We are given that xi=1, yi=2; xf=5,…

Q: Prove that (a) P(En F) = P(E)- P(En F) (b) P(EnF) =1-P(E) – P(F) + P(En F)

A: Solution: 6. Here, it is needed to prove that

Q: Property 3: The auto correlation function evaluated at the origin (t= 0) will be its maximum…

A:

Q: Let X1, . . . , Xn be iid with pdf f(x) = 1 x √ 2πθ2 e − (log(x)−θ1) 2 2θ2 , −∞ < x < ∞, and unknown…

A: Considering that  X1,X2,.........,Xn are iid with the following density as given.

Q: Use mathematical induction to prove that the n-th derivative of (x +n + 1)e" is given by d" (x+1)e =…

A: We use mathematical induction. The detailed solution is typesetted and given in detailed as the next…

Q: f(x) = (2x 0<x<1 elsewhere a. What is the joint pdf f(x1,x2, x3, x4)? b. Please calculate…

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Q: 4. Let x N (e, 1), n = 2, let T = a. 34+0² 36 b. + 17+0² 36 b. T₂ 4X₂ , RT (0) = C. 34 36 5. Let x…

A: The random variable X follows normal distribution such that X~Nθ,1 A random sample of size n=2 is…

Q: Let an m be non-negative numbers for all integers n, m > 0. Deduce Ši an,m = ΣΣ An,m n=0 m=0 m=0 n=0…

A: according to fubini's theorem if am,nm=1,n=1∞ is a doubly indexed sequence of real number then we…

Q: E (x. - x Y Show that is a consistent estimator for o is N (µ, o²).

A: ANSWER: For the given data,

Q: Let X be a random variable such that P(X= c+kh) = π(a) (poisson distribution), where c s a real and…

A: In this problem, we are given a random variable X that follows a Poisson distribution with parameter…

Q: nx 4. Let fn(x) = 1+7²², x € R. Prove that fn → 0 pointwise on R, then check whether fn → 0…

A: Since you have posted a multiple question according to guidelines I will solve first(Q4) question…

Q: Example Suppose that Y Poisson(X) and consider testing Ho: A = A ild against H₁ A Av. solve it now

A: Given: Y~Poiλ

Q: Suppose that for each i such that 1 ≤ i ≤ N one has [{ What is if N = 69? - f(t)dt = i N f(t)dt

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Q: In the expression K K - dP is evaluated? P(K – PP =] k-dt , how P(K - P)

A: To evaluate the below expression. ∫KPK−PdP

Q: Example 4: If x1, X2 , .. toking the value 1 with probability 0 and the value 0 with probability…

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Q: 2-Prove that: B (m, n)-ß (a,m) 3- Simplify to the simplest: (2+0(1-0) (1+0)(3-2)

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Q: (a) Find the auto correlation function of Y(t)

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Q: i.i.d. Consider Y₁,..., Yn Bern(p). Consider the following estimator: p = n Y with probability n-1…

A: Given information: p^=Y¯     with probability n-1nn     with probability 1n

Q: Let n EZ. Show that f(x)= x³ – nx +2 is irreducible over Q for n+-1,3,5. 72

A: Given: fx=x3-nx+2, n∈ℤ. To show fx is irreducible over ℚ for n≠-1,3,5.

Q: 9. Show that if t is a consistent estimator of e, then ť is a consistent estimator of 0°.

A:

Q: We are given A e R™** and its inverse A- E R"X: [11 2 22 2 1 1 2 22 11 2 2-2 2-3 2n-4 .... 1 -1 -1 1…

A: Condition number: The condition number of a matrix is given by, κ(A) = A∞A-1∞. Norm of matrix: The…

Q: If z = ax + by and r is the correlation co-efficient between x and y, show that o? = ao? + bo,² +…

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Q: Let T ∼ Γ (4, 0.7).   Find P(T ≥ 4). (Round the final answer to four decimal places.)

A: The objective of this question is to find the probability that a random variable T, which follows a…

Q: Let X₁,..., Xn,... (a) Prove that SA (X) = (X₂)² is consistent for . (b) Prove that dB(X) = (X₂)² -…

A: (a) To show that SA(X) = (Xn)² is consistent for , we need to show that SA(X) converges in…

Q: Suppose that X1,..., Xn are i.i.d. Poisson(0) where 0 > O is an unknown parameter. The prior T(0) on…

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Q: Use Parseval's identity to compute 1 n=0 (2n + 1)²

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Q: distributed random variables with Var(X1) < . Show that 1 n(n +1) jX; →, EX1. j=1 Note. A simple way…

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Q: 2.8 Consider the triangular random variable with pdf 0 if x 2b, if 2a < x <a+b, f(x) = X - 2a = X -…

A: In this step, we note down the given information: