Example 9-53. (a) Find the p.d.f. of X) in a random sample of size n from the exponential distribution: f(x) = a eax , a>0, x 2 0. (6) Show that X and W, = X9- X¢, r

Q: Page 263, 4.4.6.* Let X₁, X2, X3 be a random sample from a distribution of the continuous type…

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A: Given  X0.97=3

Q: 7. Derive the Wigner distribution of the signal s(t) = e+junt

A: we will use the formula of wigner distribution of any signal St  Wx,t=∫-∞∞xt+τ2×x*t-τ2×e-i2πτfdτ…

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Q: 4- Suppose that y is N3(4, 41) and let -2 -4 -1 3 -2 -3 A = 4. %3D %3D 1 y Ay, What is the…

A: Given that y~N3μ, 4𝕀 μ=123 and A=2-2-4-1341-2-3

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A: Solution: From the given information,

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Q: Question 4 Let X be a continuous random variable such that P(X 6): P(X> 6) = (Round the answer to 2…

A: P(X&lt;6)=0.1

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A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only…

Q: 2 - 4. X, X2, .. is a random sample of N (0,1), find the (X, +X,) Jox,-X2) distribution of Y

A: Solution

Q: 2. Show how the Poisson distribution -m m e (x= 0, 1, 2,...) %3D х! can be regarded as the limiting…

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Q: Let X have a Poisson distribution with a mean of 3. Define Y = (X-3) ^2 , specify pdf from Y.

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A: The mean is 5620 and the standard deviation is 429.46.

Q: (33) Let X be a random variable with p.d.f. e2k x= 1,2,3 f(x)=- find (1) k (2) E(x+1) O.W

A: Given that X is a random variable with p.d.f f(x)=e2k ; x=1,2,30     ; Otherwise.

Q: (5) Let X be a random variable with p.d.f. k 1<x<o 2 f(x) =< , find k. O.w

A: Given: fx=kx2            1&lt;x&lt;∞0                 Otherwise

Q: 20) Let X be a random variable with p.d.f. k T<x<10 f(x) =- , find k. O.w

A: Solution: Let X be the random variable with pdf f(x) is  f(x)=kx       1&lt;x&lt;100      otherwise

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Q: Example 4.2. Suppose the joint distribution of X and Y is given by 1 P(X = x, Y = y) 42 (z + y°)…

A: Solution

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A: 1) X1,X2,X3.....,Xn are the identical independent random variables from geometric…

Q: Example 4.2. Suppose the joint distribution of X and Y is given by 1 P(X = x, Y = y) 42 ; (x + y²)…

A: From the given information, PX=x,Y=y=142x+y2, I1,4xI-1,0,1,3y Consider, the two way table, Y|X 1…

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Q: If the moment-generating function of a random variable W is where t <3. (i) Write the pdf of W. (ii)…

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Q: Example 5-17. The elementary probability law of a continilolS f(x) = yoe-), asxS0, b>0, where a, b…

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Q: Problem 3) The random variable X has the following probability density function: fx(x) = {cx a) Find…

A: It is given that the random variable has the pdf fX(x) = { cx,   0 ≤ x ≤ 2        0,   otherwise }…

Q: Let X be a random variable with p.d.f. 1<x<0 f(x) =- find k. O.W

A: Given, X be a random variable with p. d. f. f(x)=12kx-2   ; 1&lt;x&lt;∞0           ; O.W. constant k…

Q: Question 1 Let X be a continuous random variable taking values in [a, b] with c.d.f. Fx which is…

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Q: 1. Let X be a random variable denoting the rate of return on the fund BancABC. The distribution X is…

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Q: (4) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x)= , find E(e2x) O.w

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Q: (34) Let X be a random variable with p.d.f. x= 1,2,3 f(x) ={ , find (1) k (2) E(²) O.w

A: X is a random variable with pdf: The sum is always 1. So,

Q: (a) Let X1 ~ x² (n, 8) and X2 ~ x² (m, 1). mX1 and its parameters. nX2 (i) Find the distribution of…

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Q: 1. Let X be a Poisson random variable on the non-negative integers with rate λ = 4. Let W = 2X + 10.…

A: