Problem involving Probability density function

[chwala]

Homework Statement

see attached

Relevant Equations

stats

I just want to be certain, i think the inequality indicated is not correct...ought to be less than. Kindly confirm...This is a textbook literature.

 

[PeroK]

In terms of continuous probability distributions $< 0.5$ and $\le 0.5$ are equivalent, because the point $0.5$ itself has zero width (or zero measure if you prefer).

 

[chwala]

In terms of continuous probability distributions $< 0.5$ and $\le 0.5$ are equivalent, because the point $0.5$ itself has zero width (or zero measure if you prefer).

Thanks Perok, so the pdf indicated above is just the same as finding the cdf at $x=0.5$ right? giving us $F(0.5)=0.125$.

 

[PeroK]

Thanks Perok, so the pdf indicated above is just the same as finding the cdf at $x=0.5$ right? giving us $F(0.5)=0.125$.

I think so. I haven't looked very carefully at the material you posted.

 

[chwala]

ought to be integral of $f(x)$ and not $x$... or is it fine the way it is?

 

[PeroK]

View attachment 299242

ought to be integral of $f(x)$ and not $x$... or is it fine the way it is?

Isn't it obvious that's a typo?

 

[chwala]

ok cheers Perok.