Continuous variables can take infinitely many values, so we use probability density functions instead of discrete probabilities. The normal distribution is most common. Learn R functions rnorm, dnorm, and pnorm to generate random draws, evaluate density, and calculate cumulative probability.
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Hi again, in the previous video we focused on discrete distributions. In this video we will talk about continuous distributions. Let's review the difference between discrete and continuous distributions using the example of a uniform distribution. A random variable from a discrete distribution can assume one of a finite number of values. There is a probability associated with obtaining each of the values. In a continuous distribution. A random variable can assume one of an infinite number of values. The probability of obtaining one specific value amounts to zero. We can calculate the probability that a continuous random variable lies within a range. In case of continuous distributions, we work with probability density functions. The density function is used to specify the probability of the random variable falling within a particular range of values. The area under the density function sums up to one. The area under the density function in a given range determines the probability that a random variable falls within that range. One of the most famous continuous distributions is the normal distribution. It's a continuous probability distribution with a bell curve shape. It is fundamental to many statistical concepts like sampling and hypothesis testing. The normal distribution is usually associated with the 6895 99.7 rule. Questions about this rule are common in interviews. The 6895 99.7 rule states that 68% of the normally distributed data lies within one standard deviation of the mean, 95% within two standard deviations of the mean, and 99.7 within three standard deviations of the mean. In the last video, we discussed the syntax of probability functions in R. Let's take a look at these functions for the normal distribution and see what they return. The RNORM function returns values on the x axis generated by the normal distribution. These values are the arguments of the density function. The denorm function returns the values on the density function and PNORM returns the area under the curve up to a specific point. The distribution can be visualized with a histogram using the HIST function. Remember that histograms do not have gaps between bars, unlike frequency charts. The lack of gaps implies an infinite number of possible values. To summarize, we've covered the difference between discrete and continuous distributions. Density functions, the normal distribution, including the 68, 95 99.7 rule, more probability functions and Histograms let's practice continuous distributions before your interview.
