For discrete random variables, one simple procedürê iš tõ list the probabilities of all pos- sible outcomes according to the values of x. Probability Distribution Function The probability distribution function, P(x), of a discrete random variable X represents the probability that X takes the value x, as a function of x. That is, P(x) = P(X = x), for all values of x We use the term probability distribution to represent probability distribution functions in this book, following the common practice. Once the probabilities have been calculated, the probability distribution function can be graphed. Example 4.1 Number of Product Sales (Probability Distribution Graph) Define and graph the probability distribution function for the number of waffles sold by a bakery in the Netherlands. This shop offers waffles that have a price of €4.00 each. Solution Let the random variable X denote the number of sales during a single hour of business from 3 to 5 P.M. The probability distribution of sales is given by Table 4.1, and Figure 4.1 is a graphical picture of the distribution. Table 4.1 Probability Distribution for Example 4.1 P(x) 0.10 0.30 2 0.20 3 0.40 Figure 4.1 Graph of Probability Distribution for Example 4.1 Probability Distribution for Waffle Sales 0.4 - 0.40 0.30 0.3 - 0.2 0.20 0.10 0.1 0.0 x (Number of Waffles Sold) From the probability distribution function, we see that, for example, the prob- ability of selling one waffle is 0.30 and the probability of selling two or more 0.60(0.20 + 0.40 ). 4.2 Probability Distributions for Discrete Random Variables 153
For discrete random variables, one simple procedürê iš tõ list the probabilities of all pos- sible outcomes according to the values of x. Probability Distribution Function The probability distribution function, P(x), of a discrete random variable X represents the probability that X takes the value x, as a function of x. That is, P(x) = P(X = x), for all values of x We use the term probability distribution to represent probability distribution functions in this book, following the common practice. Once the probabilities have been calculated, the probability distribution function can be graphed. Example 4.1 Number of Product Sales (Probability Distribution Graph) Define and graph the probability distribution function for the number of waffles sold by a bakery in the Netherlands. This shop offers waffles that have a price of €4.00 each. Solution Let the random variable X denote the number of sales during a single hour of business from 3 to 5 P.M. The probability distribution of sales is given by Table 4.1, and Figure 4.1 is a graphical picture of the distribution. Table 4.1 Probability Distribution for Example 4.1 P(x) 0.10 0.30 2 0.20 3 0.40 Figure 4.1 Graph of Probability Distribution for Example 4.1 Probability Distribution for Waffle Sales 0.4 - 0.40 0.30 0.3 - 0.2 0.20 0.10 0.1 0.0 x (Number of Waffles Sold) From the probability distribution function, we see that, for example, the prob- ability of selling one waffle is 0.30 and the probability of selling two or more 0.60(0.20 + 0.40 ). 4.2 Probability Distributions for Discrete Random Variables 153
MATLAB: An Introduction with Applications
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Question
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Ex: 4.1
I don’t know how they calculated the p(x) in table 4.1
Transcribed Image Text:For discrete random variables, one simple procedure is to list the probabilities of all pos-
sible outcomes according to the values of x.
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Table 4.1 Probability Distribution for Example 4.1
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4.2 Probability Distributions for Discrete Random Variables
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