1. The Probability Density Function of the joint Normal random variable (X,Y) N(0,) is 1 f(x,...

 

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1. The Probability Density Function of the joint Normal random variable (X,Y) N(0,) is 1 f(x, y) = e 22 ~ Prove that P(X + Y a) = 1- Density Function. -e202, and therefore f(x, y) is indeed a Probability 2. Compute the following line integral Ly dx + xdy with C being the line segment from (-5, -3) to (0,2), via (a) a t-parametrization: C = r(t), t = [0, 1]; (b) a x-parametrization (x as the parameter): C : y = mx + b; (c) a y-parametrization: C: x = ky+h. Remark: You should get the same results. 1. The Probability Density Function of the joint Normal random variable (X,Y) N(0,) is 1 f(x, y) = e 22 ~ Prove that P(X + Y a) = 1- Density Function. -e202, and therefore f(x, y) is indeed a Probability 2. Compute the following line integral Ly dx + xdy with C being the line segment from (-5, -3) to (0,2), via (a) a t-parametrization: C = r(t), t = [0, 1]; (b) a x-parametrization (x as the parameter): C : y = mx + b; (c) a y-parametrization: C: x = ky+h. Remark: You should get the same results.