2. Show that the lognormal distribution is unimodal and skewed right. Specifically, let m = = exp(μ-62) and show that a. fx is increasing on (0, m) and decreasing on (m, co), so that the mode occurs at x = m. b. f(x)0 as x → ∞o. c. f(x) →0 as x 10.

Q: Given that J h(t)dt = 8, for an even, continuous function h. Which of the following MUST be true?…

A: Please refer tge attached image for complete solution.

Q: 1. Let X1,..., X, be independent, X; ~ exp(A;). a. Show that Y = min(X1,..., Xn) is also exponential…

A:

Q: Let a, v > 0. Identify an appropriate closed curve in C in the upper half plane to evaluate ["lox:…

A: In this question, the given details are, Let a, v > 0. Identify an appropriate closed curve in C…

Q: Let g(x) [f(t) dt, where f is the function whose graph is shown. Assume g(-3) = 0. A. Compute each…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Consider the function f(x)=/25–x². a. Find the linearization L(x) of f(x) at x = 3.

A: Given function , f(x) =25-x2Linearization of f/9x/0 at x=a is given by L(x) = f(a)+(x-a) f'(a)

Q: 1. Assume f(r) is a twice continuously differentiable function on the closed interval (a, b), which…

A:

Q: 1. Find the absolute extrema on the given intervälš. a. f(x) = x3 - 6x2 +9x-8; [0,5] b. f(x) = x8/3…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: auchy's m d g(x) = e %3D

A:

Q: In(x) a) f(x) = x-1 х€ (1,00)

A:

Q: Let R be the rate at which customers are served in a queue. Suppose that R is exponential with pdf…

A: Given: Let R be the rate at which customers are served in the queue. The pdf of R is given as:…

Q: Let f(x)= x², g(x)= 2x+5, and h(x)=x² –1. Find each. 9. h[S(-2)]= 10. S[g(x-1)] =, 11.

A:

Q: Let g be a continuous function with g(2) = 5. The graph of the piecewise-linear function g', the…

A: Note:- According to our Guidelines we can provide the solution of only 3 sub parts of a question…

Q: The PDF of a continuous r.v. X is given byfX(x) = a + bx2 if 0 ≤ x ≤ 1            0 otherwise.What…

A: Given:The probability density function (PDF) fX(x):fX​(x)=a+bx2 if 0≤x≤1fX​(x)=0 otherwiseandE(X) =…

Q: Consider the Solow growth model with labor growth and no technology growth, i.e., n ‡ 0,x = 0.…

A: Approach to solving the question: To solve for the value of capital per worker at time ( t = 1 )…

Q: 11. The function f(x) is defined on [1, o0) and satisfies VTO dt. 10 Find f(x).

A:

Q: Suppose that f(x, t) is the probability of getting x suc-cesses during a time interval of length t…

A:

Q: (a) f(x) = 1 – 1; I =[-2,2] (b) f(x) = I = (1,5)

A: We will find if the given function is continuous.

Q: Consider the following pdf. 0 <x < 1 f(x) = }1/x³ 1<x<∞ Otherwise 0)

A:

Q: 20. The function f is continuous at x = 1. Vx + 3 -. - V3x + 1 for x 1 x - 1 If f(x) = k for x = 1…

A:

Q: A. What is the domain of h(x) (that is, on which x values is the functi B. Find h'(). C. At what x…

A: h(X) is defined by the integral of f(X). We need to find the domain, derivative and the relative…

Q: Determine a branch of f(2) = log(2iz – 22) that is analytic at (9) z = 1 and find f(1) and f'(1).…

A: F is a branch of f on  domain D id F is a (single valued) continuous function on D and if for all z…

Q: Suppose that a cylindrical tank initially containing Vo gallons of water drains through a bottom…

A: Toriceli's Law: Liquid flows out of a cylindrical tank with a hole at the bottom at a rate given by…

Q: 14. Given g(x) = f(t². + 6t16) dt, find intervals on increasing / decreasing and concave up/ concave…

A: The given integral function is: g(x)=∫-22x t2+6t-16 dt