CHAPTER 5 AND 6

CHAPTER 5 AND 6

1. DISTRIBUTIONS OF DISCRETE PROBABILITY

   • It is a random variable describing how probabilities are distributed between the values of the random variable. In the case of a discrete random variable x, the probability distribution is defined by a probability function, denoted by f (x). The probability function gives the probability of each value of the random variable.
     • CONDITIONS REQUIRED FOR A FUNCTION OF DISCRETE PROBABILITY

2. DISTRIBUTIONS OF CONTINUOUS PROBABILITY

   • a random variable x representing the flight time of an airplane traveling from Chicago to New York. Assume that the flight time is any value in the range of 120 minutes to 140 minutes. Since the random variable x takes any value in this interval, x is a continuous random variable and not a discrete random variable.
     • UNIFORM PROBABILITY DENSITY FUNCTION

3. Areas as a measure of probability

   • Now an observation about the graph of Figure 6.2. Consider the area under the graph of f (x) in the range of 120 to 130. This area is rectangular and the area of a rectangle is simply the width multiplied by the height. If the width of the interval is equal to 130? 120? 10 and the height is equal to the value of the probability density function f (x)? 1/20, you have, area? width ? high ? 10 (1/20)? 10 (1/20)? 10/20? 0.50.

4. Continuous random variables

   • variable that can take any numeric value within a range or collection of intervals is called a continuous random variable. Experimental results based on measurement scales such as time, weight, distance and temperature can be described by continuous random variables. Consider, for example, the experiment of observing phone calls arriving at the office of a major insurance company.

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