Another important expected value is E which is called the variance of X . For the simple coin experiment we have or by the computing formula and the standard deviation is . Note that the random variables mentioned so far have a finite set of possible values in S X . But this is an important distinguishing feature of the Poisson distribution. When a random variable can take all possible values in an interval, say , then we call X a continuous random variable because the possible values are not separated but rather continuous.
Many physical measurements are continuous such as rainfall or wind speed or humidity.
Continuous random variables require a different probability description than that used with discrete random variables because of the uncountably infinite number of possible values in the sample space. In most cases, you need to do the integration to get probabilities. Add together the probabilities of the outcomes with the same number of heads. I think the other problems are straightforward. We have added a hint to 7-10c within WebAssign.