FAQ: Introduction to Probability Distributions - Probability Density Functions

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This community-built FAQ covers the “Probability Density Functions” exercise from the lesson “Introduction to Probability Distributions”.

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This exercise can be found in the following Codecademy content:

Master Statistics with Python

Probability

FAQs on the exercise Probability Density Functions

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[henry_dodder]

I’d like to double check my interpretation of this graph. Does each point on the probability density function curve represent the individual likelihood, on the y-axis, of the event on the X-axis occurring? Given this interpretation, why wouldn’t it be possible to calculate the probability of a single point? Wouldn’t it be possible for someone to be exactly a certain height, or is that just kind of the definition of a continuous variable?

[tgrtim]

No it’s slightly different to some other probability based graphs you may have seen. The difference is that this graph is a representation of

the probability of the random variable falling within a particular range of values

Quote from Wikipedia

That mention of the range is important. I think it’s mentioned by the instructions somewhere but you can get the probability of heights between 152 and 153 cm using the area underneath this curve (an integral). In the image that would be a very thin blue strip between 152 and 153.

However any single point would effectively have an infinitely small area under the curve such that it is never observed with an effective probability of zero (assuming you had infinitely accurate measurements of height that were actually continuous).

[johannes_n]

Hello everyone!
I’ve got a question regarding the methods scipy.stats.binom.cdf(x, n, p) and scipy.stats.norm.cdf(x, mean, std):

Within this lesson we used the first one to calculate the cumulative probability of x or less coin flips. The second method we used to calculate the cumulative probability of a woman’s height less than x.

So is my understanding correct that scipy.stats.binom.cdf(x, n, p) includes x, whereas scipy.stats.norm.cdf(x, mean, std) excludes x?

Thanks a lot for any reply!