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in this video were going to talk about how to solve probability density functions so were given f of X which is 0.04 X times 5 minus X now if f is a probability density function it has to be equal to or less than zero so it cant be negative so notice that when X is zero the function will be equal to zero and also in X is five so X has to be between zero and five if X is 6 5 minus 6 will give us a negative result and if X is negative one this will give us a negative easil so X has to be between 0 and 5 now how can we verify that f is a probability density function the integral from negative infinity to infinity of any probability density function by definition has to equal 1 and since X has to be between 0 5 the integral from 0 to 5 of f of X DX must also equal to 1 so this is what we need to verify so lets integrate point 0 4 8 X 5 minus X DX from 0 to 5 and lets see if its equal to 1 so the first thing Im going to do is Im going to move this constant to the front and then I
