(a) Prove that f (x) satisfies the properties of the Pdf 8. (i) fx (x) 2 0 for all x and (ii) Jfx (x) dx = 1

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A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

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A: Given problem Given that   Some form of prophylaxis is said to be 90% effective at prevention…

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A: Given that, f(x)=x-3-2       ...(1)

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Q: 3) Let f(x)= 2x+3 . Calculate by definition f'(2).

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A: If Y=g(X) is the transformation then the PDF of Y is given by; fY(y)=fX(g-1(y))ddyg-1(y)

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A: Given f'( x ) = 2x

Q: 2) Use the Chain Rule to express the second derivative of fog in terms of the first and second…

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Q: 1. Find the derivative of the following: a) 3x²+6x f(x)= 5x-1

A: according to bartleby guide line we do only first part of multiple questions…

Q: Exercise 5: Compute / f(x)g" (x) – g(x)f"(x) dx.

A: Write the integration using two parts

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Q: B₂ (x₂3x₂ ) = 4x₁x₂ *1*2 0< x₂ <1 2 Y₁ = x₂₁² Y₂ = X₁ X/₂ Find the joint pdf for Y₁, Y₂ for 0<x< ₁…

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Q: For any function, With utilization of the product rule for functions of one variable (eq1), show /…

A: Consider the function z=f(x)·g(x) where f and g are both function of x. So we can rewrite the…

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Q: 2(x1|x2) = c1¤1/x3, 0 < x1 < x2 < 1, zero elsewhere, and f2(x2) = c2x½, 0 < x sewhere, denote,…

A: *Answer:  Give that 2. Let f12 (12) = C₁x₁/x²2, 0 &lt; x₁ &lt; x2 &lt; 1, zero elsewhere, and f2(x2)…

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

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Q: 3. a) Use the Chain Rule and the fact that |x| = Vx2 to show that d dx |x| b) Sketch the graphs of…

A: We will use the give solution as we are instructed.

Q: Let f(x) ƒ'(x) = ƒ'(3) = = √2x² + 4x + 3

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Q: (g/f)(x) f(g(x)) g(F(x)) f-1(x)

A: As per the bartleby guidelines for more than three parts only three has to be solved. Please upload…