In a game, an n-sided die is rolled once and you get, in dollars, the value rolled by the die. If the expected value you’ll get is $20, what is n?
In the actual solutions, they take an example of the previous problem to solve this. but that logic doesn’t make sense to me.
Could someone explain this problem from scratch
Assuming you’re talking about a fair die, can you start off by making a pmf?
I’m guessing it is a fair die as it isnt specified other wise. The question is as is on the quiz
Okay then can you start off by making a pmf?
Trying to figure out what function case satisfies any other number as well?
Uh no, by PMF (probability mass function) i mean something like:
For each possibility of the random variable X, i wanted you to come up with a corresponding probability for it.
(The above picture is a random image i got from google, so use that only as reference)
As a further hint, what are the odds of rolling a certain value (ofc in the defined range) on a 6 sided fair die? How would this generalize to an n sided fair die?
For n sided, wouldnt that just be 1/n .
So I did, (1/n)(n(n+1)/2) = 20
1/n for the probability
and (n*(n+1))/2) - sum of sequence
Is this correct?
sounds about right
