continuous random variable examples

Continuous random variables describe outcomes in probabilistic situations where the possible values some quantity can take form a continuum, which is often (but not always) the entire set of real numbers R \mathbb{R} R.They are the generalization of discrete random variables to uncountably infinite sets of possible outcomes.. Suppose I am interested in looking at statistics test scores from a certain college from a sample of 100 students. An example would be, let's say you play a game. Continuous Random Variables. Continuous variables are variables that measure something. Random Variables can be either Discrete or Continuous: Discrete Data can only take certain values (such as 1,2,3,4,5) Continuous Data can take any value within a range (such as a person's height) In our Introduction to Random Variables (please read that first!) So you flip a coin. My favorite example of a continuous variable is how many gallons of milk a cow gives. Note that the interpretation of each is the same as in the discrete setting, but we now have a different method of calculating them in the continuous setting. Example \(\PageIndex{2}\) At a particular gas station, gasoline is stocked in a bulk tank each week. Not all random variables are continuous or discrete. Example \(\PageIndex{1}\) We now consider the expected value and variance for continuous random variables. And with probability 1/2, you get a reward of 1/2 dollars. You can cook up random variables that are kind of neither or a mixture of the two. Continuous. we look at many examples of Discrete Random Variables. And with a certain probability, you get a certain number of dollars in your hands. Let's see another example. In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample. Let random variable \(X\) denote the proportion of the tank's capacity that is stocked in a given week, and let \(Y\) denote the proportion of the tank's capacity that is sold in the same week.

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