3. Determine the set of points at which the function 2,,2 if (, y r,y)- S continuous. if (x, y)- (0, 0 3. Determine the set of points at which the function 2,,2 if (, y r,y)- S continuous. if (x...
3. Determine the set of points at which the function f(x,y) = is continuous. (4 P.
Determine the set of points at which the function is continuous. f(x, y, z) = 7x + 2y + z D = = x, y, z) | 2 24v 7x + 2y } * Need Help? Read It Talk to a Tutor
1. Determine the set of points at which the function (r,y) = cos V1 -2- y2 is continuous. Sketch the region.
1. Let X and Y be continuous random variables with joint pr ability density function 6e2re5y İfy < 0 and x < otherwise. y, fx,y (z,y) 0 (a) [3 points] Show that the marginal density function of Y is given by 3es if y 0, 0 otherwise. fy (y) = (b) |3 poin s apute the marginal density function of X (c) [3 points] Show that E(X)Y = y) =-y-1, for y 0 (d) 13 points] Compute E(X) using the...
R programming Consider the continuous function r22r+3 ifr < 0 f(r)=r+3 12 +4 7 if 2 < x. T>r50 Write a function tmpFn which takes a single argument xVec. The function should return the vector of values of the function f(x) evaluated at the values in xVec Hence plot the function f(x) for -3 <x< 3. Consider the continuous function r22r+3 ifr
3. (a) (5 points) On the set A= R\{0}, let x ~ y if and only if x · y > 0. Is this relation an equivalence relation? Prove your answer. (b) (5 points) Let B = {1, 2, 3, 4, 5} and C = {1,3}. On the set of subsets of B, let D ~ E if and only if DAC = EnC. Is this relation an equivalence relation? Prove your answer.
Please solve the 3 questions. Question 1: Determine the set of the points at which each given function is continuous: 1) f(x,y) = (5 Marks 4-x2 - y2 (2) g(x,y,z) = In x2 + y2 - 61 Cosz (x2 - y2 + z) 3) h(x,y,z) = x + 2y - 2 x2 + y2 1
3. Suppose f : [0,) + R is a continuous function and that L limf(x) exists is a real number). Prove that f is uniformly continuous on (0,.). Suggestion: Let e > 0. Write out what the condition L = lim,+ f(t) means for this e: there erists M > 0 such that... Also write out what you are trying to prove about this e in this problem. Note that f is uniformly continuous on (0.M +1] because this is...
Problem(2) (5 points) A continuous distribution has density function k sin(r); 0rST 0; f(x) = otherwise. (a) Find the numerical value of k so that f(r) is a density function. (b) Find E[X] (c) Find E[X2. (d) Find Var X] Problem(2) (5 points) A continuous distribution has density function k sin(r); 0rST 0; f(x) = otherwise. (a) Find the numerical value of k so that f(r) is a density function. (b) Find E[X] (c) Find E[X2. (d) Find Var X]