cumulative distribution function (1 Viewer)

[stressedadfff]

hey does anyone know how to solve d

 

[stressedadfff]

also 10d please!

 

[Leadmen4y]

View attachment 30900 hey does anyone know how to solve d

integrate f(x) gives you
then sub c, giving you
multiply both sides by 2 to get rid of the denominator, equate everything to zero and use quadratic formula

you end up with 2 answers, 3/2 and 1/2
but if you draw the graph or just sub values you can see that integrating >1/2 gives you a negative value, hence c only = 1/2

 

[stressedadfff]

thank you!!

 

[Eagle Mum]

Q10d is the same function as one in the thread immediately before your’s, where it was asked how the variance of this function could be determined. https://boredofstudies.org/threads/how-would-you-find-the-variance-using-this-formula.395126/

 

[CM_Tutor]

integrate f(x) gives you
then sub c, giving you
multiply both sides by 2 to get rid of the denominator, equate everything to zero and use quadratic formula

you end up with 2 answers, 3/2 and 1/2
but if you draw the graph or just sub values you can see that integrating >1/2 gives you a negative value, hence c only = 1/2

Another way to think of this is that a PDF can never be negative, and thus

​

And, a PDF must integrate to 1 over its domain, so you need to solve

​

subject to the constraint that , and thus:

​

This approach has the advantage that it expressly addresses both the requirements for a PDF, that it always be non-negative and that it integrates over its domain to 1, and gives a reason grounded in the nature of a PDF to reject the result.