Continuous distributions
1. Continuous distributions
Hi again! In the previous video, we focused on discrete distributions. In this video, we will talk about continuous distributions.2. Discrete vs continuous
Let's review the difference between discrete and continuous distributions using the example of a uniform distribution.3. Discrete vs continuous
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.4. Discrete vs continuous
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.5. Density function
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.6. Density function
The area under the density function sums up to one.7. Density function
The area under the density function in a given range determines the probability that a random variable falls within that range.8. Normal distribution
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 68-95-99.7 rule. Questions about this rule are common in interviews.9. 68–95–99.7 rule
The 68-95-99.7 rule states that 68% of the normally distributed data lies within one standard deviation of the mean,10. 68–95–99.7 rule
95% within two standard deviations of the mean,11. 68–95–99.7 rule
and 99.7% within three standard deviations of the mean.12. Probability functions
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.13. Probability functions
The dnorm function returns the values on the density function.14. Probability functions
And pnorm returns the area under the curve up to a specific point.15. Histogram
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.16. Summary
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.17. Let's practice!
Let's practice continuous distributions before your interview!Create Your Free Account
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