Hello, this is my first time posting here. I am studying for the P1 actuarial exam
Thank you for any help
X = # of times you need to roll to get the first 5.
E(X ∣ X > 2) = (1/(1/6)) + 2
How do I get this ^ solution ^
Hello, this is my first time posting here. I am studying for the P1 actuarial exam
Thank you for any help
X = # of times you need to roll to get the first 5.
E(X ∣ X > 2) = (1/(1/6)) + 2
How do I get this ^ solution ^
Lets assume you are talking rolling a fair die. The prior history of rolls does not effect the future outcomes, so:
$\displaystyle E(X|X>2)=E(X)+2$
and:
$\displaystyle \displaystyle E(X)=\sum_{k=1}^{\infty} k \left(\frac{5}{6}\right)^{k-1}\frac{1}{6}=\frac{1}{6} \sum_{k=1}^{\infty} k \left(\frac{5}{6}\right)^{k-1}$
CB