Check that the standard normal PDF p(x)=e-r²/v2™ satisfies the equation I xp(x)dx = p(y). y>0. By using this equation and sin x= ,' cos ydy, or otherwise, prove that if X is an N(0, 1) random variable, then (Ecos X) < Var (sin X) < E(cos X).

Q: Find the equation of the normal line of f(x) = x⁴ + 2x at x = 1 using the limits definition.

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Q: Let X1,...,X, be a random sample from (1+ 0x) f(x) = 2 ,-1< x < 1, -1 < 0 < 1. Find the consistent…

A: The random sample consists of X1,X2,...,Xn. Need to obtain: The consistent estimator of θ. The…

Q: Let X1, ... , Xn be a random sample have the pdf 1 (1-0) f(x,0) = -(x),0 < x < 1, 0<0 < ∞. Find mle…

A: The likelihood of X1,X2,...,Xn is given as: L=∏i=1nfxi,θ=∏i=1n1θxi1-θθ=1θ∏i=1nxi1-θθ…

Q: I sin 2x cos 2x + kog log a|+e] Ans. y de Jogx

A: Given,

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A: Period of the signal is 2. So using Nyquist criterion the appropriate sampling time will be half of…

Q: Let X1,..., Xn be iid pdf (log(æ)-®1)² 262 1 f(x) -00 < x < o0, and unknown parameters 01 and 02.…

A: Let X1,X2, X3...be iid with pdf, f(x)=1x2πθ2e-(log(x)-θ1)22 θ2          -∞&lt;x&lt;∞   The…

Q: (a) Let X be a random variable with PDF ƒ(x) = 1−|x|, |x| ≤ 1. Obtain the MGF of X. (b) Find the PDF…

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Q: Estimate the probability distribution given the empirical equation for Normal Distribution below…

A: To estimate the probability distribution from x1 = -2 up to x2 = 1.6 using Romberg Integration, we…

Q: Use the table to determine D,f(g(x))) at x= 3. 3 4 f(x) 1 f(x) 3 -5 8(x) 2 g'(x) |1 4 3 2 4 1 3 6 -5…

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Q: If f(x)=5+2(x-1)^1/2, does f(x) satisfy all the conditions of the mean value theorem in the interval…

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Q: (a) flx,g;Z) =

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Q: Find the equation of normal to the function f(x) = x³ - 3x + 1 at its local maximum point.

A: The objective of this question is to find the equation of the normal line to the given function at…

Q: Let ƒ(x) = − 2 sin¯¹(e8²) ƒ'(x) =

A: Given query is to find indicated derivative.

Q: Find solution of the problem in the form of the normal mode u * eo-xlc) and discuss the result a²u…

A: Given that : u=eiw(t-xc) Simplify it, we get : u=eiwt.e-iwxc. We know that : eiθ=cosθ+i.sinθ .…

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: What is the value of the beta function, B(x, y), where x and y are positive real numbers?

A: We have to write the value of the beta function, B(x, y), where x and y are positive real numbers!

Q: write the equation of normal line for xsiny = cos(x+y) at ( 112, 0)

A: To find equation of normal line

Q: 1. Let the random variable Y have pdf as f(y\A) = e®=e=t(e-1), y>0,1>0. Show that W = e – 1] ~ x²…

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Q: Suppose that {Xk} k=1,...,n are i.i.d ∼ Exp(λ), the pdf is given by f(x) = λe^(-λx), x > 0. Let Y1…

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Q: Let f(x) = 6x4 In(x) + 3 ,5 2. 5 f'(x) = ||

A: The objective is to find the derivative.

Q: Find the maximum likelihood estimator for θ in the pdf f(y; θ) = 2y/(1 − θ^2), θ ≤ y ≤ 1.

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Q: Equation of the line normal to function f(x) = (x-8)2/3 + 1 at P(0, 5) is %3D

A: We use the formula ,the equation of normal line is y-y1=m(x-x1) where m is the slope.

Q: (a) Calculate the median of X. (b) Note: No need to show the second derivative. Calculate the mode…

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Q: sing g(x)d/dx[f(x)]-f(x)d/dx[g(x)]/ [g(x)]^2 , find the derivatie of y = xe^x-2x+4/x-2 and simplify…

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Q: What is the average value of f(x), between x = 0 and x = 5 for f(x) = 2 + sin(x)?

A: The average value of f(x) between x=a to x= b  is     dx

Q: d) Determine the equation of the normal line to the graph of the function y+z*v = z sin(u") + vye"…

A: According to the given information, it is required to find the equation of normal line of the given…

Q: OP(X sa) = P (X >a) (ii) P (X > b) = 0.1 %3D

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Q: Prove that √ ²07²dx = √= So e

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Q: =tX > 0. The random variable X has moment generating function 1 Mx(t): t<λ. " [1 − (t/X)]² ¹ Use…

A: Solution

Q: Suppose that that the RV X has the Gamma(2,β ) distribution for some β > = 0, E(X) = 2β and V (X) =…

A: Given that the RV X has the  distribution for some ,  and .Given , the RV Y has the  distribution.

Q: O A random process is given by X(t) =P+Q cos(@t+ 0) where P, Q are independent random ables. The…

A: Given information: Given that the random process is X(t) = P + Q cos(wt + θ). The mean and variance…

Q: Which of f (x) = x sin2 x and g(x) = x2 sin2 x has a larger average value over [0, 1]? Over [1, 2]?

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Q: Let 7(t) = Find 7'(t) デ'() = Answer preview:

A: We have to solve