12. Suppose the PDF is given by f(x) = Cx² for 1 ≤ x ≤ 2, and zero otherwise. (a) Find the value of C. (b) Find the likelihood that a point selected at random with respect to this PDF is between 1.5 and 2. (c) With X (x) = x, find E(X) and Var(X).

Q: Show that the function f(x) = e¯*/2 has inflection points x = f1. at

A: We have the given function as fx=e-x22              ⋯⋯1 As we know that, a point of inflection of…

Q: f(x) = (x² + In x)(x³ + 4x + 5) f(x) = (x2+5x) In x (Vx-6x)e* %3D

A: We have to find the derivative for each of the functions. 1. fx=x2+lnxx3+4x+52. f(x)=x2+5xlnxx-6xex

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: Let f(x) f'(2)= | ƒ' (6)= Lomm 7 Vx Evaluate each of the following: I

A:

Q: If ƒ(x) = (x² + 3x + f'(x) = + 3x + 2)², then ƒ' (2) =

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: 16. What is the best point estimate of the population mean? A. The sample mean B. The sample median…

A: A single statistic result is called a point estimate of a population parameter.

Q: The number of representatives of a political party, N, in a city council depends on the percentage…

A:

Q: Find the stationary points of the function f(r) = 3rª – 2rº. Apply the Second Derivative Test to…

A: Given function is fx=3x4-2x6. Stationary point is the point where first derivative of the function…

Q: Suppose f is differentiable and (-1,4) is a point on the graph of f. The estimate f(-0.8) 5 is…

A:

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: If f(x)=5+2(x-1)^1/2, does f(x) satisfy all the conditions of the mean value theorem in the interval…

A:

Q: 6x erivative of f(x) equal to zero, calculate x*: f'(x*) = 0. Using the second derivative ther x* is…

A:

Q: d dx f(x)=sina, f(0) = 7.

A:

Q: Is the function given by g(x) = x²-3x continuous at x = 4? Why or why not?

A:

Q: Use the Mean Value Theorem to prove that f'(x) = 0.01 has a solution in the (-4, -3) interval.…

A: We use cubic formula to calculate the value of c

Q: If F(x)= 27 0<x <3 then pdf f(x): 9. .2 9X II

A: F(X)=x327 , 0&lt;x&lt;3we have to find probability density function.

Q: 3. Differentiate. x²e* f(x)%3= x² + ex

A:

Q: If f(x) = 4 ln(5 + x), ƒ'(x) = ƒ'(1) =

A: f(x)=4ln(5+x)

Q: 3. Consider the function f(x) = e¯*. 4x2 – 2 (a) Show that the second derivative is f"(x) (b) Find…

A:

Q: 4. Consider f(x) = 6 + (x+3) ²/³. Find the extrema of this function using the first derivative test.

A: We have to find extrema by first derivative test.

Q: 7. Determine where the function is continuous. (a) f(x) = 1+x (b) g(x) = sinx+x² + x + 1. x² (c)…

A: This is a problem related to continuity of thr function. Please follow the procedure given below.

Q: Find (f1)'(3) given the following table of values. f(z) f'(z) 3 1

A: The given table is, x fx f'x 2 3 1 This means that, At x=2,   fx=3   and  f'(x)=1. That is,…

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: (d) At any time, find the mean age of insects in the population.   (e) Sketch g(x), the p.d.f. of…

A: From the given The data used to draw : x h(x) 0 0 1 0.0202 2 0.0417 3 0.0660 4 0.0952…

Q: 6. Consider this prefix expression: +1A-BC+D* EF (a) Write in postfix form. (b) Write in infix form…

A:

Q: 1. The figure shows the graph of the derivative f' of a function f. (a) On what intervals is f…

A: Since the student has posted multiple questions and does not mention any specific question, so we…