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In today’s topic I want to explain how we plot the distribution of a random discrete variable.

**Key terms:** expected mean, probability, variance and standard deviation.

Let’s explain it by an example. For rolling a Die, let us assume a random variable X (x=1,2,3,4,5,6). The probability is P(x) =1/6. That is exactly same for all outcomes.

So, if we put it into a plot, it should look like:

This is also called uniform probability distribution. Let us know calculate the expected value or mean = summation of xp(x).

Variance = Summation of (*x* – *µ*)^{2} P(*X* = *x*)

Standard deviation = Square root of the variance.

Now, we can easily calculate the expected mean for this example and also variance by using mean and probability. The variance or standard deviation is important for calculating the spread of the distribution. In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own boolean-valued outcome.

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