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

Q: Evaluate y' of the given functions: 1. y = (x² – 2)(x + 3)

A:

Q: TRUE / FALSE) For two pdfs f(x) and g(x), f(x)g(x) is a pdf.

A: Solution

Q: Screen Shot 2021-10-05 at 9.01.21 AM.png y = (3 Vx – x2 + 2)x5 33 x9/2 – 7x6 + 10x* 2 - 33 x7/2 –…

A: See the details solution in below

Q: x²+16x Let f(x) : = *+16x Find the value of x such that the tangent line to y = f(x) is horizontal.…

A: We know slope is given by derivative of f(x) w.r.t. x And tangent line is horizontal When slope is…

Q: 6) Use derivatives to find where the function is concave up f(x)=x.e2x*

A: If  f "(x) &gt; 0  on an interval, then f(x) is concave up on that interval.

Q: Differentiate the function. h(t) = √t-8e* h'(t)

A:

Q: Suppose that the p.d.f. of X is as given f(x) = 3(1-x)2 for 0<x<1 and 0 otherwise Find the pdf of…

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)

Q: For the function f(x) x + x3, find all of the relative and absolute extrema using the first or…

A:

Q: Calculate the derivative of the following function. y=f(g (5x*)), where f and g are differentiable…

A:

Q: Suppose you are rolling a die for 4 times. Let x be the random variable finding how many times you…

A: a) Given that the die will be rolled 4 times. So the possible values of x is= 0, 1, 2, 3, 4.

Q: Find the derivatives of function 1–xy x (x.0) 1+xVx

A:

Q: Excrcise 10. Find the derivative d -7x * [" (t³ + 2) dt dx

A: Given,          ddxx∫57xt3+2dt

Q: Suppose that f(x) is a function with f(180) = 35 and f'(180) = 10. Estimate f(180.5). f(180.5)

A:

Q: Suppose that f(x) is a function with f(130) = 39 and f'(130) = 2. Estimate f(132).

A: f(x) is a function with f(130)=39 and f′(130)=2

Q: Show that the function f(x) = exp(-|x|) is not differentiable at x = 0.

A: Given function is  fx=e-x given point is x=0.

Q: 4. Find the derivative of r°(x+ 1)² y = Vr – 3x2 |

A: First i i have written the quotient rule of derivative , just use them for given function and get…