X, defined over the range (1, ∞) has pdf given by: f(x) = 2/x3 Calculate E(x),...

X, defined over the range (1, ∞) has pdf given by:

f(x) = 2/x³

Calculate E(x), E(x²) and Var(x)
Calculate E(X/5) E[(X/5)²] and Var(X/5)

Expert Solution

I think I got the PDF right if it is not so then please mention your PDF properly.

orchestra answered 2 years ago

6) Given: (a) f (x) = (2x^2)/(x^2 −1) - Calculate f ′(x) and f ″(x) -...

6) Given: (a) f (x) = (2x^2)/(x^2 −1) - Calculate f ′(x) and f ″(x) - Determine any symmetry - Find the x- and y-intercepts - Use lim f (x) x→−∞ and lim f (x) x→+∞ to determine the end behavior - Locate any vertical asymptotes - Locate any horizontal asymptotes - Find all intervals where f (x) is increasing and decreasing - Find the open intervals where f (x) is concave up or concave down

consider the function f(x) = 1 + x3 e-.3x a. what is f'(x) b. what is f''(x)...

consider the function f(x) = 1 + x3 e-.3x a. what is f'(x) b. what is f''(x) c. what are the critical points of f(x) d. are the critical points a local min or local max or neither? e. find the inflection points f. if we define f(x) to have the domain of [2,50] compute the global extreme of f(x) on that interval

(1) z=ln(x^2+y^2), y=e^x. find ∂z/∂x and dz/dx. (2) f(x1, x2, x3) = x1^2*x2+3sqrt(x3), x1 = sqrt(x3),...

(1) z=ln(x^2+y^2), y=e^x. find ∂z/∂x and dz/dx. (2) f(x1, x2, x3) = x1^2*x2+3sqrt(x3), x1 = sqrt(x3), x2 = lnx3. find ∂f/∂x3, and df/dx3.

A joint pdf is defined as f(x) =cxy for x in [1,2] and y in [4,5]...

A joint pdf is defined as f(x) =cxy for x in [1,2] and y in [4,5] (a) What is the value of the constant c? (b) Are X and Y independent? Explain. (c) What is the covariance oc X and Y? i.e. Cov(X ,Y)

Let X1, ..., Xn be iid with pdf f(x; θ) = (1/ x√ 2π) e(-(logx- theta)^2)...

Let X1, ..., Xn be iid with pdf f(x; θ) = (1/ x√ 2π) e(-(logx- theta)^2) /2 Ix>0 for θ ∈ R. (a) (15 points) Find the MLE of θ. (b) (10 points) If we are testing H0 : θ = 0 vs Ha : θ != 0. Provide a formula for the likelihood ratio test statistic λ(X). (c) (5 points) Denote the MLE as ˆθ. Show that λ(X) is can be written as a decreasing function of | ˆθ|...

Let X and Y have the joint pdf f(x,y)=(3/2)x^2 (1-|y|) , -1<x<1, -1<y<1. Calculate Var(X). Calculate...

Let X and Y have the joint pdf f(x,y)=(3/2)x^2 (1-|y|) , -1<x<1, -1<y<1. Calculate Var(X). Calculate Var(Y). P(−X≤Y).

Let X1, X2, X3 be continuous random variables with joint pdf f(X1, X2, X3)= 2 if...

Let X1, X2, X3 be continuous random variables with joint pdf f(X1, X2, X3)= 2 if 1<X1<2 -1<X2<0 -X2-1<X3<0 0 otherwise Find Cov(X2, X3)

Expand the function, f(x) = x, defined over the interval 0 <x <2, in terms of:...

Expand the function, f(x) = x, defined over the interval 0 <x <2, in terms of: A Fourier sine series, using an odd extension of f(x) and A Fourier cosine series, using an even extension of f(x)

The joint PDF of X and Y is given by f(x, y) = C, (0< x<y<1)....

The joint PDF of X and Y is given by f(x, y) = C, (0< x<y<1). a) Determine the value of C b) Determine the marginal distribution of X and compute E(X) and Var(X) c) Determine the marginal distribution of Y and compute E(Y) and Var(Y) d) Compute the correlation coefficient between X and Y

Given f(x) = 1 x 2 − 1 , f 0 (x) = −2x (x 2...

Given f(x) = 1 x 2 − 1 , f 0 (x) = −2x (x 2 − 1)2 and f 00(x) = 2(3x 2 + 1) (x 2 − 1)3 . (a) [2 marks] Find the x-intercept and the y-intercept of f, if any. (b) [3 marks] Find the horizontal and vertical asymptotes for the graph of y = f(x). (c) [4 marks] Determine the intervals where f is increasing, decreasing, and find the point(s) of relative extrema, if any....

Question