Applied Statistics and Probability for Engineers
5-3 TWO CONTINUOUS RANDOM VARIABLES 157 5-3 TWO CONTINUOUS RANDOM VARIABLES 5-3.1 Joint Probability Distributions Our presentati ...
158 CHAPTER 5 JOINT PROBABILITY DISTRIBUTIONS At the start of this chapter, the lengths of different dimensions of an injection- ...
5-3 TWO CONTINUOUS RANDOM VARIABLES 159 The probability that is determined as the integral over the darkly shaded region in Fig. ...
160 CHAPTER 5 JOINT PROBABILITY DISTRIBUTIONS (5-17) and where RXdenotes the set of all points in the range of (X, Y) for which ...
5-3 TWO CONTINUOUS RANDOM VARIABLES 161 The first integral is The second integral is Therefore, Alternatively, the probability c ...
162 CHAPTER 5 JOINT PROBABILITY DISTRIBUTIONS We have obtained the marginal probability density function of Y. Now, 5-3.3 Condit ...
5-3 TWO CONTINUOUS RANDOM VARIABLES 163 This is an exponential distribution with 0.003. Now, for the conditional probability ...
164 CHAPTER 5 JOINT PROBABILITY DISTRIBUTIONS EXAMPLE 5-18 For the random variables that denote times in Example 5-15, determine ...
5-3 TWO CONTINUOUS RANDOM VARIABLES 165 5-34. Determine the value of csuch that the function f(x,y)cxyfor 0x3 and 0y3 satis ...
166 CHAPTER 5 JOINT PROBABILITY DISTRIBUTIONS 5-36. Continuation of Exercise 5-34. Determine the following: (a) Marginal probabi ...
5-4 MULTIPLE CONTINUOUS RANDOM VARIABLES 167 5-4 MULTIPLE CONTINUOUS RANDOM VARIABLES As for discrete random variables, in some ...
168 CHAPTER 5 JOINT PROBABILITY DISTRIBUTIONS The requested probability is P(X 1 1000,X 2 1000,X 3 1000,X 4 1000), which equ ...
5-4 MULTIPLE CONTINUOUS RANDOM VARIABLES 169 As for two random variables, a probability involving only one random variable, say, ...
170 CHAPTER 5 JOINT PROBABILITY DISTRIBUTIONS The concept of independence can be extended to multiple continuous random variable ...
5-5 COVARIANCE AND CORRELATION 171 EXERCISES FOR SECTION 5–4 5-55. Suppose the random variables X, Y, and Zhave the joint probab ...
172 CHAPTER 5 JOINT PROBABILITY DISTRIBUTIONS That is, E[h(X,Y)] can be thought of as the weighted average of h(x,y) for each po ...
5-5 COVARIANCE AND CORRELATION 173 If the points in the joint probability distribution of Xand Ythat receive positive probabil- ...
174 CHAPTER 5 JOINT PROBABILITY DISTRIBUTIONS Now Therefore, EXAMPLE 5-28 In Example 5-1, the random variables Xand Yare the num ...
5-5 COVARIANCE AND CORRELATION 175 If the points in the joint probability distribution of Xand Ythat receive positive probabil- ...
176 CHAPTER 5 JOINT PROBABILITY DISTRIBUTIONS If Xand Yare independent random variables, XYXY 0 (5-31) EXAMPLE 5-31 For the ...
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