A function is defined as follows: y = X + 6 x² 3x + 1 X<-2 -2<x<3 x > 3 For which x-values is f(x) = 4? Select all that apply 0-2 1 2. 13 e here to search
3.98 Let X be a continuous random variable with probability density function f(x) defined on = {xl-π/2 < x < π/2). Give an expression for VIsinX)
A periodic function f(x) with period 21 is defined by: X + -1<x< 0 2 f(x) = 0<x< 2 Determine the Fourier expansion of the periodic function f(x). X - TT
5. Let be the function defined by f(x) = -1 3 1.5 if r <0 if 0<x<2 if 3 < r <5 Find the Lebesgue integral of f over (-10,10).
6. Let g(t) = { 2te** t 20 6. Let g(t) be the probability density function of the continuous 0 t<0 random variable X. a. Verify that g(t) is indeed a probability density function. [8] b. Find the median of X, i.e. the number m such that P(x = m) = { = 0.5. [7]
4. [10 pts] Let X be a random variable with probability density function if 1 < a < 2, 2 f(a)a 0 otherwise. Find E(log X). Note: Throughout this course, log = loge.
Determine if the following piecewise defined function is differentiable at x = 0. x20 f(x) = 4x-2, x2 + 4x-2, x<0 What is the right-hand derivative of the given function? f(0+h)-f(0) lim (Type an integer or a simplified fraction. I h h+0+
2. Let X have probability density function JX2) = 1/2 0<x< 1 3 < x < 4 otherwise Find the cumulative distribution function of X.
1. Let X and Y be random variables with joint probability density function flora)-S 1 (2 - xy) for 0 < x < 1, and 0 <y <1 elsewhere Find the conditional probability P(x > ]\Y < ).
Find the length od the curve C defined by х = t2/2 - Int, y = 2t for 1 <t <2.