1) Let Y= x² Find cdf and PDF 2) Let Y= e, Find cdf and PDF

Q: 2. Construct the CDF of X if the pdf is given by f(x) = (1 − ²) (2,6)(x).

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Q: d) the conditional pdf of Y given X. e) E(Y|X = -1)

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Q: Let fx(x) = x + b, x € [-2b,2b]. For which b is fx(x) a pdf?

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Q: I'(x) p-let dt,

A: Γ 12=2×∫0∞e-u2 du Here, Let's calculate the value of Γ 12, The gamma function is defined as Γ…

Q: Q/ Let f(x, y) = 4(x + y) 3 5 x is pdf with 1<x<∞ 0≤y<1

A: Given information: fx,y=4x+y5x3, 1&lt;x&lt;∞, 0&lt;y&lt;1

Q: 1. Compute E(1/X) 2. Find the cdf and the pdf of Y = 1/X 3. Compute E(Y) and compare this result…

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Q: If X and Y have joint pdf given by

A: From the given information, fX,Yx,y=2I0,yxI0,1y                =2, 0&lt;x&lt;y, 0&lt;y&lt;1

Q: Verify Young's Theorem y? x2 z = In(2x + y) + +e(x+2y) y

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Q: verify that w xy= w yx. w = e^x + x ln y + y ln x

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Q: 3) Suppose the joint pdf of lifetimes of a certain part and spare is given by f(x,y) = {e**), 0 < x…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: (i) Find the conditional pdf's fyx2 and X y

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Q: Prove the relationship =<- dt

A: we have to calculate  ddt&lt;px&gt;  .....(1) &lt;px&gt;=-ih∫ψ*∂ψ∂xdx .....(2) substituting equation…

Q: Let fx (x) = x +b, x ∈ [−2b, 2b]. For which b is fX (x) a pdf?

A: Given,  fx (x) = x +b, x ∈ [−2b, 2b] To find the value of b for which fX (x) is a pdf.

Q: 6.5.4 Find the PDF of W = X + Y when X and Y have the joint PDF fx,x(z,y) • otherwise.

A: Given: The joint probability density function of the random variables X and Y is provided as:…

Q: ) Consider the joint pdf fxy (x, y) = cxy, for 0 < x < 3,0 < y < x a) Determine the value of c so…

A: The pdf given isfx,y=cxy                         ,0&lt;x&lt;3;0&lt;y&lt;x   a) If the pdf is valid,…

Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: Given function is y=sin4 cosz. To find the derivative of the given functions. Solution: Chain rule…

Q: Find the indicated derivative. dp for p q² + 2 5q – 3 %3D dq dp dq II

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Q: Let f (x, y) = 4 xy n² (n + 1)² is joint pdf with x,y=1,2,3,...,n then V(x/y) is

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Q: Suppose that the joint pdf of X1 and X2 is given by fx1,x2(*1, 2) = 1/x1, 0 < x2 < ¤1 <1 and 0…

A: Given, X1, X2 are two random variables, with the joint pdf       fx1,x2 given.

Q: compute the derivative R(s) = sln s

A: Given the function R(s) = sln s

Q: Find the d. c. of from definition. Vx

A: As per the question we have to find the derivative of the function : f(x) = 1/√x Using the limit…

Q: Calculate the covariance and correlation between X and Y. dint: Use the computational formula to…

A: Solution: The joint PMF of (X, Y)   value of Y    14 22 30 40 65 Total  Value of X 1 0.02…

Q: compute the derivative. y = z csc(9z + 1)

A: y=z csc9z+1

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rcos(r) (3…

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Q: Find du -if v = t- dt

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Q: Let X1,· , Xn be iid with pdf 1 -(x-01)/02, x > 01, -∞ 0. 02 f(x|01, 02) Show that (Xn – X1)/(X2 –…

A: Given that X1, X2, ...., Xn is iid with PDF, fx|θ1, θ2=1θ2e-x-θ1θ2,   x&gt;θ1 A statistics is…

Q: Write a chain rule formula for the following derivative. du for u = f(x); x = g(p, q, r) ar du du ar…

A: We have to choose correct option

Q: Find the equation of the normal line to the curve f (x) = 6e2x cos x at the point (0,6). %3D

A: Now point on the function is (0,6 ) . Step 1 : find the value of the derivative at x=0 . So, f(x) =…

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: 5. Two ballpoint pens are selected at random from a box that contains 3 blue pens, 2 red pens and 3…

A: Joint probability mass function : The joint probability mass function is a function that fully…

Q: Suppose X and Y have the joint pdf f (x, y) = c(1.57 – x – y), x+y 0, y > 0 - a) Find the value of…

A: Introduction: The joint density function of two random variables X and Y is given below: (a). Find…

Q: Let Y and Y have the joint pdf f (x,y) = 6(1– x – y), x+ y < 1, 0 < x, 0 < y, zero elsewhere.

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: 2. Find the normal equations to the curve 2* = ax + bx + c %3D 2 = ax+ bx + c

A: Apply normal equation formula as below

Q: suppose the cdf of r.v. X is given by 1- e -2 x x > 0 F(x) = x < 0 Please find its pdf, and compute…

A: It was stated to suppose that X is a random variable. The given CDF is as follows:  Fx=1-e-2x ;…

Q: Prove ¬(3x € X : (Vy ¤ Y : E(x, y))) = \x € X : (‡y ¤ Y : ¬E(x,y)) (Vx X: (³y € Y : E(x, y))) = (3x…

A: We have to prove  a) ¬∃x∈X : ∀y∈Y : Ex, y=∀x∈X : ∃y∈Y : ¬Ex, y b) ¬∀x∈X : ∃y∈Y : Ex, y=∃x∈X : ∀y∈Y :…

Q: Suppose we have a fair spinner with the numbers 1,2, and 3 on it. Let X be the number of spins until…

A: Solution

Q: Find the joint characteristic function of X and Y if SxY (x, y) = 1 exp

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Q: Let f (x, y) = csc(x + y³) ey , find дудх

A: The given function is  f(x,y)=csc(x+y3)exy. The main objective is to evaluate ∂2f∂y∂x.

Q: = ze'y = e+z'e= C to denote an arbitrary constant.)

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Q: Example Find the F.T of rectangular pulse (%) To - f(t) = A rec T %3D

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Q: Sheet 4 Numerical analysis dx QI/ Evaluate Jo 1+x2 Simpson's 1/3 rule Simpson's 3/8 rule i- ii-

A: In the question we have to find value of integrals.

Q: Consider the joint pdf fxx (x, y) = cxy, for 0<x<3, 0<y<x a) Determine the value of c. b) Find the…

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Q: find y In x+Vx

A: Topic- differentiation

Q: Example Find the F.T of rectangular pulse To - f(t) = A rec T

A: Given query is to find the Fourier Transformation of the expression.

Q: If X and Y have the joint pdf fxx(x. y) 20sx<ys 1 fr(1/2) = fxpy-1/2(1/6) P(0<X<1/8 Y-1/2)

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Q: Let T be a statistic, then T is sufficient statistic for 0 if the conditional pdf f(0,x1, X2,..…

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Q: Prove that (x – 2)dx = – f,(x – 2)dx |

A: To prove that:∫13x-2dx=-∫31x-2dx

Q: It follows that the pdf of Y is

A: It is given that the  X has a geometric distribution with parameter p i.e. X~G(p) and fX(x) =qxp ;…