Problem 1. Suppose the joint PDF of X and Y are given by f(x, y) = Are X and Y independent? Justify. 24xy for x ≥ 0, y ≥ 0, x + y ≤ 1 0 otherwise

Q: 2. The graph of the derivative f' of a function f is shown. (1)On what intervals is f increasing or…

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Q: 1. a) Find the successive derivatives of the following functions: (x' +80x²)* ii) Z (x* +10x +20) 21…

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Q: Suppose that a PDF for a continuous variable X is given by if 0 x)=3/4

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Q: 5.1-2. Let X have the pdf f(x) Find the pdf of Y = X². = xe-x/2,0 < x < 00

A: Given

Q: 20. True or false (If true mark "a" and if false mark "b"): The amplitude of y = secx is 1.

A: Given; y=secx

Q: 5) Find if y = (cos h x)* dx

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Q: If some function f(x) has a relative extrema at the point (c, f(c)), then f'(c) = 0 True False

A: if we want to fine any fuction has relative extrema then

Q: Q1) Answer the questions by true or false 1) If y = In then the derivative of y is = (x2 + 3) * 2x…

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Q: If y = xsin then y is equal to = X" at x =

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Q: 5. Let X have the pdf f(x) = 5x¹, 0 < x < 1, zero elsewhere. Find the pdf of Y = - 2ln(X).

A: The random variable X has the pdf given below: fx=5x4,   0&lt;x&lt;1 The transformed variable is…

Q: d) Suppose that f(x) and g(x) are differentiable functions and that h(x) = f(x)g(x). You %3D are…

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Q: X Dx f¹2dt 4+t -X

A: We have to differentiate the given equation.

Q: Problem3: Let X and Y have the joint pdf f(x, y) = 6(1 - x - y), x + y< 1,0 < x, 0 <y, zero…

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Q: Find df / dx and of / dy. f(x,y) = elx +y+7) (x +y +7) of I dx =

A: Given : fx,y = ex+y+7

Q: 5. What is the derivative of the given function below? * x² + y² = xy dy dy dx dx Option, dy dx = =…

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Q: 4) The median of the pdf f (x) = x 1,2,3, .7 is equal to 5 a. True b. False 5) The value of the…

A: Note : Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: 6) When some variable z is a function of time (t), the derivative of z with respect to t is denoted…

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Q: 1. Find derivative, critical numbers and the absolute maximum and absolute minimum values of f(z) =…

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Q: Find the derivative of y with respect to x. 1/9x²-1 + sec -13x, x> y= cot %3D

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Q: An equation for the line tangent to the graph of the differentiable function f at x = 3 is y = 4x +…

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Q: AP style question 6. Suppose f is a twice- differentiable function such that f(2) = 5 and f (5) = 2.…

A: Let f be a twice differentiable function such that  f(2)=5f(5)=2 Let g be the function given by…

Q: The Mean Value Theorem for problem 3 says that between x=-2 and x=2, there exists a value x=c that…

A: Let, y=f(x) =27-x2Now , f(-2) =27-(-2)2  =27-4=23   and f(2) = 27-22  =  27-4=23   and…