If a,b,c,d are in continued properties,prove that

Q: 4. If {X(t)} is a WSS process and if Y(t) = | h(u)X(t – u)du, then Ry,(T) = R„(T)* K(t), K(t) =…

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Q: 2. If the member functions of a Gaussian process are uncorrelated, then they are independent.

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Q: (3) P(A| B) > 0, i.e., the conditional probability is always non-negative.

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Q: Prove that for every integer n > 2, P(n+1, 3) = n³ . %3D -n.

A: Given to prove that for every integer n≥2,  Pn+1, 3=n3-n. We shall prove this by the method of…

Q: If F(s) = 1/(S-2), then f(t) is %3D a) e²'u(t) c) u(t-2) d) e"'u(t) -2t b) u(t +2)

A: Given Fs=1s−2 We have to find the ft Use definition of inverse Laplace transform, which is given…

Q: It states that if a sample space S has N mutually exclusive events B, n=1,2,....,N, such that, B,…

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Q: If the characteristic function of a RV X is f,(@) and if Y = aX + b, then O,(@) = ibo e

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Q: Theorem: let S₁, S₂ be the collection of sets D (US) U (US). = US. SES, VS₂

A: Solution: Let S1  and S2  be  the  collection of sets.We  have  to show  that  ∪S∈S1S∪∪ sS∈S2=∪…

Q: 8) Suppose A E Mnxn(F) is diagonalizable. Let A1,· , Ak be the (distinct) eigenvalues of A. a) Prove…

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Q: 5. If the number of occurrences of an event E is an interval of length t is a Poisson process {X(t)}…

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Q: The spectral density function of a real random process is an even function.

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Q: Let A be a non-empty set of positive numbers, which is bounded above and let B = {x e R: 1/x e A}.…

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Q: 29. For any odd integer n, n° n² +3 %3D 4 4

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Q: 3. If (X(t)} is a WSS process and if 00 Y(t) = | h(u) X(t – u)du, then - 00 (i) Ry (t) = R(T)* h(-t)…

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Q: (5) If two events A and B are mutually exclusive, then the joint events, AnC and BOC are also…

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Q: (b) If m < a1 + ... + an < M n, and v, is positive and + anVn < Mv1. + anUn| < Mvi Vn. decreasing,…

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Q: Given: F(s) = (2s+3)/(s² -2s +5). Evaluate: f(1) Use 2 decimal places. 5.67

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Q: 1. If a Gaussian process is wide-sense stationary, it is also strict-sense stationary.

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Q: Let R be a ring such that for each a eR there exists XE R such that a'x = a. Prove the following :…

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Q: The interarrival time of a Poisson process, i.e., the interval between two successive occurrences of…

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Q: Additive property: Sum of two independent Poisson processes is a Poisson process.

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Q: 4. If R(T) is the autocorrelation function of a stationary process {X(t)} with no periodic…

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Q: The coefficient of correlation is independent of the change of origin and scale of measurements.

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Q: Consider a sample space S that has N mutually exclusive events B, n=1,2,...,N , such that BB, = {Ø}…

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Q: 1. The Poisson process is a Markov process.

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Q: Let (X, M, μ) be a measure space and (Y, 7) be a topological space. Let f: X→Y be a function. Set Ω…

A: Definition : Let X be any set  and F be a collection of subsets of X . We say that F is a σ- algebra…

Q: Multiplication theorem can be used to find out the probability of outcomes when an experiment is…

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Q: -) Let dim(V) = n. Let T : V → V be a linear operator. Let W1, W2 C V e T-invariant subspaces.…

A: given dimV=n , W1,W2⊂ V be a T-invariant subspace. suppose V=W1⊕W2 let β1=w1,w2,....wk be an ordered…

Q: 1) a. The number of mobile phones made by Finland has the following probability distribution: А 2 +…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.