why those terms are equal after By convexity
why those terms are equal after By convexity f(x) = x log x By convexity, -...
5. (a) Show that if the functions f and g are log-convex, f+g is also log-convex. Give a counter example to show that this is not true for log-concave functions (Hint: log(f +g)log(elogf +elogs). Show that this is convex by the second-order test for convexity.) (Hint: Use the definition of log-convex functions.) (Note: Harmonic mean of a,b is defined as T^T.) b) Suppose f is convex, g is non-decreasing and log-convex. Show that h(x) g(f(x)) is log-convex. (c) Show that...
Express in terms of sums and differences of logarithms. x82 log 13 8 log x + log 2-3 log y 8 log x.log 2-3 logy log (8x + 2) - 3 log y (log x)8 + log z- (logy) 3 Express as a single logarithm and, if possible, simplify. logax +4 loga y - 2 loga x loga Vay4 loga y4 x3/2 loga x2y4 loga x4y4
6. Derivatives!! ITEMS 12. (1 point) Differentiate f (x) = log, X. f'(x) = Submit answer Answers Your answer
In question 5, f(x) = λ*exp(-λx), for x greater or equal to 0, and zero otherwise. 9. Let X have an exponential distribution with λ = 1 (see Question 5), and let Y = log(X). Find the probability density function of Y. Where is the density non-zero? Note that in this course, log refers to the log base e, or natural log, often symbolized In. The distribution of Y is called the (standard) Gumbel, or extreme value distribution. 2
A)Find the inverse of the function f(x)=3+{2x-1 B) SOLVE log(x+2)+log 3 (x-2)=2 5. 6. vords e here to search ORI
QUESTION 1 (x + x2)log x + x2.5 is ou O x2 log x O X3 O x2 O x log x QUESTION 2 If f(x) is O(g(x)) and g(x) is O(h(x)) then f(x) is O(h(x)). True False
Explain why we cannot estimate a linear-log or log-log version of the regression (i.e. where the independent variables are logged). finpro f i-β0+ β 1 treatment i + β 2 perc female+ β, perc momsec+ β 4 perc dadsectu finpro f i-β0+ β 1 treatment i + β 2 perc female+ β, perc momsec+ β 4 perc dadsectu
Let S f(w)dt = 6, f(x)dx = -4, log(x)dt = 12, 9(x) dx = 9 Use these values to evaluate the given definite integral: -3 (f(x) f(x) + g(x)) dx
Given f(x) = 2 log(x) – 2, find f-1(-8). b) 27 c) 27 d) -3 e) 3 f) None of the above.
c) log,6-log, (2x + 3)-log, (x + 1) d) 2log, x - 3 + log, (x-2) 2.