# Probability distribution essay

While it’s possible to look up probabilities for a normal distribution using the z-table , it’s actually much easier to calculate probabilities in Excel for a couple of reasons. First, there’s no looking at a table; the NORMDIST function does the hard work for you. Second, Excel does the intermediate calculations for you. Most calculation errors happen in an intermediate step (such as calculating the z-score to look up) rather than the actual z-score itself. Excel can handle three types of probability calculations: more than, less than, and in between. These instructions work for Excel 2007 and Excel 2010.

In other respects, the probability density function of a continuous random variables behaves just like the probability mass function for a discrete random variable, where we just need to use integrals rather than sums. For a function $\rho(x)$ to be valid probability density function, $\rho(x)$ must be non-negative for each possible value $x$. Just as for discrete random variable, a continuous random variable must take on some value in the set of possible values with probability one. In this case, we require that $\rho(x)$ must integral to one. In equations, the requirenments are \begin{gather*} \rho(x) \ge 0 \quad \text{for all $x$}\\ \int \rho(x)dx = 1, \end{gather*} where the integral is implicitly over all possible values of $X$.