## Create a binomial probability distribution and histogram

The experiments of flipping a fair coin three times and observing the genders of children in a randomly chosen three-child family are completely different, but the random variables that count the number of heads in the coin toss and the number of boys in the family (assuming the two genders are equally likely) are the same random variable.
Figure 4.4 “Probability Distribution for Three Coins and Three Children” provides a histogram that graphically portrays this probability distribution. The two experiments have one thing in common: we conduct three identical and independent trials of the same action, each with just two outcomes (heads or tails, boy or girl), and the likelihood of success is the same, 0.5, on each trial. The created random variable is known as the binomial random variable. In a success/failure experiment, a random variable that counts successes in a set number of independent, similar trials. with n = 3 and p = 0.5 as parameters This is only one example of a larger problem.

## Discrete random variable using statcrunch

A curve is the graph of a continuous probability distribution. The region under the curve represents probability. This definition was introduced in Chapter 2 when we used histograms to establish relative frequencies. The probability of drawing at random an observation in that category was the relative region for a range of values. The graph in Example 4.14, like the Poisson distribution in Chapter 4, used boxes to describe the likelihood of unique values of the random variable. Since the random variables of a Poisson distribution are independent, whole numbers, and a box has width, we were being a little careless in this situation. The points along the horizontal axis, the random variable x, were intentionally not labelled on the axis. Since the area under a point is zero, the probability of a given value of a continuous random variable is zero. Probability equals surface area.
The probability density function is the name of the curve (abbreviated as pdf). The curve is defined by the symbol f(x). f(x) is the graph’s corresponding function; we use the density function f(x) to draw the probability distribution graph.