So far we have been finding probabilities of discrete outcomes. However, methods for discrete probability distribution do not work with continuous data.
Let’s say that city bus arrives every 12 minutes: if I arrive at the bus stop at a random time, we can wait anywhere from 0 minutes up to 12 minutes. So our wait time is continuous not discrete (i.e. we may have to wait for 0 minutes, 0.1 minutes, 1minute, 1.4 minutes and so on), and there are an infinite number of minutes we may have to wait. WE therefore cannot create bars (like we did for visualizing discrete distribution). We use a continuous line to represent probability, and its the same probability for waiting anywhere from 0 to 12 minutes:
If we wish to find the probability that we would have to wait for anywhere between 4 to 7 minutes, i.e. $P(4 \le wait \; time \le 7)$: we can use the area to compute the same, as shown below:
For continuous data, counting the number of possible options would be impossible. Instead, we need to focus on a the probability of getting a particular range, and a particular level of accuracy.
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Sample Space of continuous distribution is infinite, due to this, we cannot record the frequency of each distinct value and cannot represent it in a tabular format. We can however, represent a continuous distribution by drawing the graph of a probability distribution function.
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Above was an example of Continuous Uniform Distribution, where each outcome has the same probability, but it can take forms other than uniform where some outcomes have a higher probability than others. Below is an example of Bimodal Distribution, where two values occur frequently and there are 2 modes.
Another example is a Normal Distribution which has a peak in the middle:
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Regardless of the shape of the distribution, the area under the curve is always 1.
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