6 vector RVs. 6-1: probability distribution A radio transmitter sends a signal to a receiver using three paths. Let X1, X2, and X3 be the signals that.

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6 vector RVs

6-1: probability distribution A radio transmitter sends a signal to a receiver using three paths. Let X1, X2, and X3 be the signals that arrive at the receiver along each path, whose joint CDF is known. Find the probability that maximum signal is less than or equal to 5. Find the probability that X1 is less than of equal to 5

6-2: joint pmf

6-3: joint pdf Let X 1 be uniform in [0, 1], X 2 be uniform in [0,X 1 ], and X 3 be uniform in [0,X 2 ]. Note that X 3 is also the product of three uniform random variables. Find the joint pdf of X and the marginal pdf of X 3.

6-4: joint characteristic function Suppose U and V are independent zero- mean, unit-variance Gaussian random variables X = U+V Y = 2U+V Find the joint characteristic function of X and Y, and find E[XY].