V(t) 2 Draw the probability distribution and probability density functions of a periodic voltage signal given in the figure (the figure is an isosceles triangle) 1- T t

Question 1 function given by Suppose that X and Y have a joint probability density if x, y ≥ 0 otherwise fx,y(x, y) = (a) Verify that fx,y is indeed a probability density function. (b) Find the marginal probability density function fx and state the name of the distribution of X. 7e-x-7y (c) Find the conditional probability density function fy|x=x- (d) Are the random variables X and Y independent? Justify your answer. (e) Let another probabilty density fx,y be given by Sce-(√+√y)²+2√y - {e fx.y (x, y) = if x ≥ y ≥0 otherwise Determine the normalization constant c in this case. Are X and Y statistically independent? Justify your answer.

Section: Probabilty Density Functions