I was asked to give an example of a random variable which has finite $i$'th moments for $i=1,2,\ldots,k$ and has an unbounded $(k+1)$th moment.
Obviously, a Student-distributed $t_{k+1}$ random variable will work, but I suppose giving a proof link to Wikipedia is not an option, and dealing with density which involves Gamma function is far beyond my current level of maths.
- Is there a simpler way to show the desired property for Student distribution? If not,
- Are there any simpler examples of random variables with this desired property?
Thank you very much in advance!