Pick two consecutive integers x, y. Assume that m= xy. Assume that g=max(x,y). Prove that m+g...
Assume X and Y are lognormally distributed, prove that XY is lognormally distributed.
Let g, h be two real-valued convex functions on R. Let m(x) = max{h(x), g(x)). Prove that m(x) is also convex 3.
3. The maximum of two numbers x and y is denoted by max(x, y). Thus max(-1,3) max(3,3) - 3 and max(-1,-4) denoted by min(x, y). Prove that max(-4,-1) - -1. The minimum of x and y is max(z, y)ly- min(x, ) ty ly- max(x, y, z) -max(x, max(v, z) 2 (2a) (2b) Derive a formula for max(x, y, z) and min(x, y, 2), using, for example
4. Two integers are consecutive if, and only if, one is one more than the other. Prove the following statement: The difference of the squares of any two consecutive integers is odd. [8 points]
4. Consider the functions f : R2 R2 and g R2 R2 given by f(x, y) (x, xy) and g(x, y)-(x2 + y, x + y) (a) Prove that f and g are differentiable everywhere. You may use the theorem you stated in (b) Call F-fog. Properly use the Chain Rule to prove that F is differentiable at the point question (1c). (1,1), and write F'(1, 1) as a Jacobian matrix.
4. Consider the functions f : R2 R2 and...
The product of two consecutive integers is 42. Find all such pairs of integers. The positive set of integers: x = and x+1 = The negative set of integers: x = and x+1 =
prove if two random variable are indpendent then cov(x,y)=0 without using E(xy)=E(x)E(y) this property?
Q1/ Use algebraic manipulation to prove that (xy)(x y) x
find the sum of the reciprocals of two consecutive even integers if the smaller integer is x.
Prove that the elasticity of Y with respect to X is equal to-2 XY