Answers both of them, please. The joint density function for a pair of random variables X and Y is given. (Round your answers to four decimal places.)f(x, y)- Cx(1 + y) if 0 s xs 5, 0 s ys 2otherwise(a) Find the value of the constant C.| 1/96(b) Find P(X S 1, Y< 1).3/384(c) Find P(X + YS 1).1/72 (a) A lamp has two bulbs, each of a type with average lifetime 1,500 hours. Assuming that we can model the probability of failure of a bulb by an exponential density function withmean u = 1,500, find the probability that both of the lamp's bulbs fail within 1,200 hours. (Round your answer to four decimal places.)(b) Another lamp has just one bulb of the same type as in part (a). If one bulb burns out and is replaced by a bulb of the same type, find the probability that the two bulbs fail within atotal of 1,200 hours. (Round your answer to four decimal places.)

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The joint density function for a pair of random variables X and Y is given. (Round your answers to four decimal places.) (ax(1 + y) if o sxs 5, 0 s ys 2 f(x, y) otherwise (a) Find the value of the constant C. 1/96 (b) Find P(X S 1, YS 1). 3/384 (c) Find P(X + YS 1). 1/72

The joint density function for a pair of random variables X and Y is given. (Round your answers to four decimal places.) (ax(1 + y) if o sxs 5, 0 s ys 2 f(x, y) otherwise (a) Find the value of the constant C. 1/96 (b) Find P(X S 1, YS 1). 3/384 (c) Find P(X + YS 1). 1/72

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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