trice Poage, January 20, 2016 2: Find the intervals wherc this function is continuous: 32 -4,...
2. Find the value of c so that the function is continuous everywhere. f(x) = 02 – 22 r<2 1+c => 2 {
[4 Pts. Use the definition of continuity to show that the function f is continuous at <=0 10 g(x)= 3-4
X with density fcx)3/56 ir 2<<4 5. Consider a continuous random variable X with density f(x)- otherwise a. Find P(1 <X<3) b. Find ECX)
(4) Find the Laplace transform of this function: Set if 0 <t <2, 0 if 2 <t.
(2x - 1 if x < -1 2. Suppose f(x) = 2x2 - 4 if-1<x52 (log: (x - 1) if x > 2 a) Is f continuous at x = -1? Justify your answer completely. b) Is f continuous at x = 22 Justify your answer completely. 3. Suppose f(x) = x2 + 3x a) Using the definition of derivative, find f'(x). No credit will be given if shortcuts are used. b) Find the equation of the tangent line to...
If 4 - x2 = f(x) < 4+x2 for –3 <x<3, find lim (2) 20
Find the constant a such that the function is continuous on the entire real line. f(x) = [ 5x2, x 21 ax - 5, x < 1 a =
6. Let X be a continuous random variable whose probability density function is: 0, x <0, x20.5 Find the median un the mode. 7. Let X be a continuous random variable whose cumulative distribution function is: F(x) = 0.1x, ja 0S$s10, Find 1) the densitv function of random variable U-12-X. 0, ja x<0, I, ja x>10.
121 Q1. If x is continuous variable and follows probability density function x/7; 2<x<4 f(x) = then find the value of P(2<x<3) ? 0; otherwise
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.