Applied Statistics and Probability for Engineers
59 3 Discrete Random Variables and Probability Distributions CHAPTER OUTLINE LEARNING OBJECTIVES After careful study of this cha ...
60 CHAPTER 3 DISCRETE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS 3-1 DISCRETE RANDOM VARIABLES Many physical systems can be ...
3-2 PROBABILITY DISTRIBUTIONS AND PROBABILITY MASS FUNCTIONS 61 For each of the following exercises, determine the range (pos- s ...
62 CHAPTER 3 DISCRETE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS For example, in Example 3-4, and Check that the sum of the ...
3-3 CUMULATIVE DISTRIBUTION FUNCTIONS 63 3-13. The sample space of a random experiment is {a,b,c, d,e,f}, and each outcome is eq ...
64 CHAPTER 3 DISCRETE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS Clearly, these three events are mutually exclusive. Therefo ...
3-3 CUMULATIVE DISTRIBUTION FUNCTIONS 65 Figure 3-3 displays a plot of From the plot, the only points that receive nonzero proba ...
66 CHAPTER 3 DISCRETE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS 3-29. Determine the cumulative distribution function for th ...
3-4 MEAN AND VARIANCE OF A DISCRETE RANDOM VARIABLE 67 The mean of a discrete random variable Xis a weighted average of the poss ...
68 CHAPTER 3 DISCRETE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS Now Although Xnever assumes the value 0.4, the weighted ave ...
3-4 MEAN AND VARIANCE OF A DISCRETE RANDOM VARIABLE 69 EXAMPLE 3-11 The number of messages sent per hour over a computer network ...
70 CHAPTER 3 DISCRETE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS Suppose Xis a discrete uniform random variable on the conse ...
3-5 DISCRETE UNIFORM DISTRIBUTION 71 EXAMPLE 3-14 As in Example 3-1, let the random variable Xdenote the number of the 48 voice ...
72 CHAPTER 3 DISCRETE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS 3-6 BINOMIAL DISTRIBUTION Consider the following random exp ...
The event that X 2 consists of the six outcomes: Using the assumption that the trials are independent, the probability of {EEOO ...
As in Example 3-16, equals the total number of different sequences of trials that contain xsuccesses and nxfailures. The total ...
3-6 BINOMIAL DISTRIBUTION 75 general distribution, which includes the binomial as a special case, is the multinomial distributio ...
76 CHAPTER 3 DISCRETE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS If Xis a binomial random variable with parameters pand n, ...
mial random variable with p0.001. If 1000 bits are trans- mitted, determine the following: (a) (b) (c) (d) mean and variance of ...
3-7 GEOMETRIC AND NEGATIVE BINOMIAL DISTRIBUTIONS 3-7.1 Geometric Distribution Consider a random experiment that is closely rela ...
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