The joint PDF of the r.v. A and B is constant on (a, b): a, b > 0n 0.5 < x + y < 1, and is 0 outside. Find P(Y>0.5|X<0.5).

Q: Oz Aradom Variable(x) has the following cof FX(X) = (x³ + x) al find the pdf of X find Pro <xcot)…

A: Given that: The cdf of random variable X is given as: FxX=12X3+X      where 0≤X≤1

Q: a.) If f(x)= sin(In(x* )), find f'(x). b.) If g(x) = 5x find g'(x). %3D .2 x +3

A: (a) Consider the provided function, fx=sinlnx3 Find the derivative of the provided function. Apply…

Q: Let P(x) dt. Evaluate 2 | P(x)dx. sin

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Q: A fair coin is tossed two times independently. Let H₁ = {1₁ (1, if head is obtained at the ith toss…

A: When head is obtained at 1st toss then H1= 1  When head is not obtained at 1st toss then  H1= 0 When…

Q: QO use best linear approximation to (F(Xiy) = ²³ to estimate the value of f at the point (0.0),…

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Q: If SeF dr = [c(-5x + 3y² ) dx + (x³y) dy, what is F? %3D F =

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Q: b) Suppose that f is the Expon(5) PDF. Compute SLf(x) dx.

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Q: f(x) = 1 + 3x² –- 2.x³ Find the local maximum and minimum values of f using both the First and…

A: To Determine: find the local maximum and minimum values of f using both first derivative and second…

Q: Let v = (2, (2, 3, 2) 3,

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Q: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

Q: cx? if – a (x) = 0 otherwise a = 3.89, what is c?

A: The probability density function f(x) has the property that the total area under the density…

Q: S f(t) dx = 0. 1.

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Q: Decide whether or not the real function In (eon 2) I+0, = (1) 1= 0, is continuous at r = 0.

A: The given function is fx=ln cos2x2x2     if  x≠0-1                if  x=0. Compute the limit…

Q: Prove that Jn (x) X good dx=1. n

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Q: The function f(x) = Ei-1 Cix;| is piecewise linear and convex. True O False

A: Step:- 1 Convex piece-wise Linear: - A function f: ℝn→ℝis a convex piece-wise linear if there exist…

Q: |х — 1 x5

A: Use the method of substitution to evaluate the integral. I=∫x−1x5dx=∫x−1x52dxLet u=xdu=12xdxSo,…

Q: [cos x - sin x 01 If f (x) = | sin x 0, show that f(a)f(b) = f(a + b). 11 cos x

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Q: Let f(x)= (x²e* )/2 for x> 0, and zero otherwise. Show that f(x) is a pdf. b. Find the mean. Hint:…

A: The given function is:

Q: Let f(x.y) = In (x2y). If f,(2,1)=f,(5,a) what is the value of a? O a. -1 O b. 1 Oc. 0 Od.-2 e. 2

A: From the given problem:   fx,y=lnx2y   fx2,1=fy5,a   Now,   fx=∂f∂x=∂ ∂ xlnx2y=1x2y∂ ∂ xx2y=1x2y·…

Q: For the function y = x² + 2x, the value of dy when *=3 and dx=0.1 js -0.15 A) 0.15 B) C) - 0.8 0.8…

A: We will find out the required value.

Q: 1-ス 17+4 キ文T AND FIMD

A: Given that:x=t+t-1 and y=t2+t-2

Q: Let f(x,y) = In (x2y). If f,(2,1)=f,(5,a) what is the value of a? O a. -1 O b. 1 O.0 O d.-2 O e. 2

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Q: 3) Find a value of c for which f(x) is a pdf on the indicated interval. Q11 f(x) =, [0, 1] 1+x2

A: We know that the total probability is always 1. Using that we get:

Q: Suppose X - Uniform (0,1). Find the CDF and PDF of Y = InX.

A: To find the cumulative distribution function (CDF) and probability density function (PDF) of the…

Q: Find all values c in (−64, 64) such that f '(c) = 0.

A: From given information, it can be predicted that f(-64) = 0 f(64) = 0 To Find : all values c in (64,…

Q: b) Evaluate f v1 – x² dx.

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Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 16/x on the interval [0,…

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Q: Let T ∼ Γ (4, 0.7).   Find P(T ≥ 4). (Round the final answer to four decimal places.)

A: The objective of this question is to find the probability that a random variable T, which follows a…

Q: Let f(x.y) = In (x³y) . If f(6,2)=f,(5,a) what is the value of a? O a 1 O b. -1 Oc. 0 Od. 2 O e. -2

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Q: 4- 13 + 6y = 0 dx

A: We have to be find