(5) If two events A and B are mutually exclusive, then the joint events, AnC and BOC are also mutually exclusive and hence P((AUB)|C) = P(A|C)+ P(B\C)

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: Suppose A and B are bounded and nonempty subsets of real numbers and 1 E R. In this case: sup(A U B)…

A: Let A,B not empty, bounded subsets of R .Prove thatsup(A∪B)=max{sup(A),sup(B)}. Let: ⇒x∈A∪B⇒x∈A or…

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

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Q: 4. Give an example of an indefinite quadratic form on R³ whose corresponding symmetric matrix has no…

A: Let Q(x1,x2,x3)=-x12-2x1x2+6x1x2+3x22-2x2x3-x32 be a quadratic form whose symmetric matrix is…

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

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Q: eimil 2.5 THEOREM Suppose f : D R and g : D→ R, xo is an accumulation point of D, and f and g have…

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Q: Property 2: The auto correlation function Ryx (t) is an even function of t, i.e., Ryx (t) = Rxx (-…

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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: [Problem 1] Prove the following statements formally. a) Let f(n) b) Let f(n) = = log2 (n) and g(n) =…

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

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Q: Property 1. Algebraic sum of the deviations of a set of values from their arithmetic mean IS zero.…

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Q: Prove the property.

A: To prove,

Q: tan? Asin? A= tan? A-sin?A %3D

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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: Please prove it

A: Given information: The investigator is specially interested to estimate the parameter u of a…

Q: Let f [a, b] → R be a bounded function. Then the followings are equivalent. (a) f [a, b] → R is…

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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: If Hof(x); p) = F(p), then Milaihaq Holf(x-a) H(x-a); pl = [q ni=-00 of faqesh diw. (ii) yiliga nall

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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: Prove that all even perfect numbers n is of the form (2-1)2P-1, where 2P-1 is prime. 11

A: Given: 2p-1 is prime. To Prove: All even perfect numbers n is of the form 2p-12p-1.

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

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Q: (b) If S is a set of content zero in RP, then its closure 5 (union of the boundary of S and interior…

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