(a) A random variable X has pdf fx(x) = " 1 (z/0) /2, 0

Q: Let f (x) = f₁²² sin² (t)dt. Find ƒ' (π). ○ 2π sin² (π) π sin² (7²) ○ sin² (²) ○ 2π sin² (²)

A: The given function is

Q: 1. (Review) (a) Suppose that X~ Cauchya and c> 0. Show that Y = CX ~ Cauchyca (Hint: This is a…

A: Given: X ~ Cauchya Thus, the PDF of X is given by: fX (x) = aπ.(a2 + x2)   for  x∈ℝ Now, the random…

Q: 3. Suppose 1500 runners are in a race. How many ways could the runners finish in 1t, 2nd and 3rd…

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Q: et d Calculate dt \e +1) ()

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: Let f(æ) = In a*(x + 5)*(2² + 4)*| f'(x) =

A: We will use properties of logarithm. lnan = n lna  ln(a.b) = lna + lnb

Q: X is an exponential random such that fr(x) e. If the linear random variable transformation is made…

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Q: Let f(x) = cos t dt ,x> 0. Then Ax) has (a) maxima when n = - 2, - 4,- 6, . . . . (b) minima when n…

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Q: A. If G(2) = F(z) · H(z), then G' (3): %3D B. If G(w) = F(w)/H(w), then G' (3)

A: Given F(3)=1, F'(3)=2, H(3)=4, H'(3)=1.

Q: Consider one-parameter members of exponential family of the form, 8(yl0)= exp{d(@)+S(y)+c(0)T(y)},…

A: Given See the handwritten solution

Q: Let X have cdf Fx(x) = 1- (1+x)^-A, x,a > 0. Determine the pdf and cdf of Y = CX

A: Let X have cdf Fx(x) = 1- (1+x)^-A, x,a > 0

Q: Let f(t) = 4t* – 4t + 5e'. Then f'(t) =

A: find the derivative

Q: A technology manufacturing company has recently switched to the production of isolinear processors.…

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Q: Now fx,(x) = *(0,)(x), and Fx₁(x) =(1-e1⁰0*)(0, ∞)(x);

A: Given,f(x)=1100e-1100x         ; 0<X<∞

Q: Let X(t) be a stationary continuous random process that is differentiate. Denote its time derivative…

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Q: Prove that if f'(z)=0 then f(z) is a constant.

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Q: If F()dt= x*, then f(8) = %3D (A) 32 (B) 0

A: Given: By Euler's formula for integral,              ddx∫0x3f(t)dt=ddx(x4)⇒f(x3)…

Q: How do i find e(x), var(x) and e(x^3) using the moment generating function

A: Let us define the random variable X with moment generating function Mx(t).The moment generating…

Q: The bivariate beta type I pdf is fx,„x, (x1, x2) = Kx-x" (1 – x1 – x2)e-!, x1 > 0, x2 > 0 and x1 +…

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Q: Q1)A nisy transmission channel has a per digit error probability Pe=001 Calculate the propability of…

A: Note: As per guidelines ,we are supposed to solve only one question at a time. please repost the…

Q: 5 (i) Let x,, ..., x„ be a random sample from x„) is sufficient for 0? the PDF f(x: 0). What is…

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Q: Example 11: 3 If F(x) = J Int dt, find F'(xr) 2+sin 2.x

A: To determine the F'(x).

Q: Let f(æ) = In(z') f'(2) =

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Q: The joint pdf of Y, and Y, is given by (a) ,with support (b) , and 0 elsewhere. (a) 1/y2; (b) 0 < y…

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Q: x f(x) f'(x) g(x) g'(x) 1 1 1 3 3 4 3 65 1 3 -2 3 4 4-2 -6 51 6 The functions f and g have…

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Q: Suppose X₁ and X₂ have the joint par f(x1, x₂) fw (w) For constants w₁ > 0 and w₂ > 0, let W = W₁X₁…

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Q: Let F (x) = (1 + t2)/5 dt - Then F'(x) =

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Q: Assume that X and Y have joint pdf x + 3x?y if 0 }). 1. Simplify the final expression as much as…

A: Thus, P(X≤1/2 and Y ≥1/2) =3/8 =0.375

Q: 1 If F(x)= - 00 <x <0 the pdf f(x)= 1+e-x -X e (1+e¯X) e (1+e¬x)² Oe* 1+e*

A: Given: F(x)=11+e-x , -∞&lt;x&lt;∞ To determine: The pdf f (x) of F (x).

Q: - 3 Let f(x) = 8xVæ + x2. f'(x) =

A: Use the derivative for finding the answer.

Q: (b) Verify mean value theorem for f(x)=x² - 5x+6 over the interval [1,3].

A:

Q: 6. If f(x,y) = 2 x>0; y>0; x+y<1 Show the conditional pdf of Y given x is uniform.

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Q: Let f(x) = 1 + x³ + dt. Determine the value of (f-1)'(0).

A: