R Tutorial: Density and cumulative density

Want to learn more? Take the full course at https://learn.datacamp.com/courses/foundations-of-probability-in-r at your own pace. More than a video, you'll learn hands-on coding & quickly apply skills to your daily work. --- When you flip a fair coin ten times, what's the most likely number of heads? Well, since heads and tails are equally likely, you can probably figure out that the most likely outcome is that 5 come up heads, 5 tails. Say I offer you a bet: if it is exactly that result, I'll pay you a dollar, otherwise you'll pay me a dollar. Should you take the bet? To answer this, we'll have to find the probability a binomial variable X with these parameters- ten flips, each with a 50% probability- results in an outcome of 5. We would express this as "Pr X equals 5." One way to find out is to simulate many draws from X- say, a hundred thousand: and then see how common each outcome is. As you saw in the last exercises, you can choose the number of simulations to perform by setting the first argument of rbinom. This resulting variable flips then contains the results of these one hundred thousand draws. We can't print out all these results, at least not in a way we'll understand them. Instead, we can visualize them in a graph. This plot is called a histogram: each bar shows the relative frequency of one outcome, from 0, 1, 2 all the way through 10. Histograms are a common way to examine a probability distribution, and we'll be using them frequently throughout the course. Notice that out of these hundred thousand draws, about twenty five thousand are equal to 5. There's a useful trick in R for calculating the fraction equal to 5 directly. The expression flips == 5 compares each item in the vector to 5. We can then use the mean() function to find the fraction of comparisons that are TRUE. This works because the mean function treats TRUE as 1 and FALSE as 0. Thus, "mean flips == 5" gives the fraction of values equal to 5. You're going to be using this trick with