Recent content by cjaylee

Let the joint PDF of (X,Y) be of the form: f(x,y) = 1/8x(x-y), 0<=x<=2, |y|<=x f(x,y) = 0 elsewhere Find P(X+Y<=2). The answer that my teacher gave was P(X+Y<=2)=∫01dx ∫-xx 1/8x(x-y)dy + ∫12dx ∫-x2-x 1/8x(x-y)dy I do not understand how my teacher could separate the integral like...

Homework Statement Use the limit definition of derivative to determine the derivative of the following function: f(x) = { sqrt(x^2+1) if x<=0 0 if x>0 Homework Equations I'm not sure as to why the function is not continuous at x=0, and so it's not differentiable at that...

Oh okay. Thanks.

It says in the text that if f'>0, then f is increasing and if f'<0, then f is decreasing on the interval?

If f and g are both decreasing, then f'<0 and g'<0. Is that right? And if both the slopes are decreasing, then f''<0 and g''<0?

Homework Statement (a) If f and g are positive, increasing, concave upward functions on I, show that the product function fg is concave upward on I. (b)Show that part (a) remains true if f and g are both decreasing. Homework Equations - The Attempt at a Solution (a) f>0...

Hey. I am quite confused by continuity and derivatives. Both are finding the limits of a particular function as x approaches a. Then why is it that a graph that is continuous cannot be differentiable? If it is continuous, it means that the limit exists and so, it should be differentiable right?