Estadistica Descriptiva

Probability distributions
Determining probabilties for varius types of events is simplified if we can Estbalish a general model used to obtain probabilities is called a probability distribution. A model is generally a simplified representation of some other thing. When a model uses mathematical models. They are also functions as defined in chapter 2 an can be called probabilitys functions. If weselect a probability function that accurately represents the experiment of interest then the function provides probabilities for the events in the sample space of the experiment. The accuracy of these probabilities depends on how well thw model fits the situation. There are several well-known probability distibutions that are suitable for a wide range of apllications. We will study the mostcommon of these in this chapter. However, before looking at specific distributions we must first consider the meaning of the term random variable

Random variables

In chapter 1 and 2 we discussed variables. We defined a variable as being some quantitative characteristic that varies over a set . we can continue to think of a variable in this way but we should refine that concept slightly to includerandom variables. A random variable is a variable whose values are determined by the outcome of an experiment
We will continue to use the ntation adopted in previous chapters by designating random variables whit lowercase letters, usually in the latter part of the alphabet specific-values of a random variable are indicated by the use of subscripts such as ….. and so on
If a random variable isdefined a a variable whose value is determined by the outcome of an experiment consists of tossing a coin one time.. the two possible outcomes of this experiment are head and tail if we let the random variable x represent the possible values, that is …….. we find that it is more convenient to specify values of a random variable if a head occurs and the value 0 if a head fails to occur. Then ifwe define the random variable x as representing the number of heads that occur on the ross of a coin x can have the value 1 or 0 when all of the values of a random variable are numbers we a numerical random variable .
Suppose we define a new experiment consists of four coin tosses. We can say that the new experiment consist of four trials of the original experiment. We still define the randomvariable x as representing the number of heads that occur during this experiment, that is on four tosses in this new experiment x can have the value 0 1 2 3 or 4 each possible value of x correspond to an event in the sample space of the experiment but no necessarily to a single outcome. The possible outcomes in the sample space of this experiment and their conrrespondence to the possible values of xare shown in table 8.1
In this experiment the possible vlues of x are limited to certain numbers specifically 0 1 2 3 and 4 when the random variable is limited to certain values it is called a discrete random variable remember that in chapter 1 we defined a discrete variable as one that is restricted to certain values within some range of values. There are experiments in which the randomvariable is not limited to certain discrete values but can assume any value within some range of values. Observations of outcomes in an experiment of this type are measurements. As an illustration, consider an experiment in which 16-ounce cans of fruit juice are weighed asthey come off a production line. The weighing process assures that each can contains the correct amount of juice. The weight ofeach can is indicated by the position of a pointer on a very precise scale although it is necessary to read and record every weight in terms of discrete units, ounce, tenths of ounces etc the actual weight of the can is nopt limited to any of these discrete values if the scale can be read to the hundredth of an ounce a reading of 16.02 means that the true weigth of the can may be anywhere between...