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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 X1 be uniform in [0, 1], X2 be uniform in [0,X1], and X3 be uniform in [0,X2]. • Note that X3 is also the product of three uniform random variables. • Find the joint pdf of X and the marginal pdf of X3. 6-4: joint characteristic function • Suppose U and V are independent zeromean, unit-variance Gaussian random variables • X = U+V • Y = 2U+V • Find the joint characteristic function of X and Y, and find E[XY]. 6-5: sum of geometric RVs 6-6: central limit theorem • Suppose that orders at a restaurant are iid random variables with mean ($8) and standard deviation ($2). • Estimate the probability that the first 100 customers spend a total of more than $840. • Estimate the probability that the first 100 customers spend a total of between $780 and $820. • After how many orders can we be 90% sure that the total spent by all customers is more than $1000?