I am having trouble with this question with regards to random variables and calculating expected values:
Suppose I keep tossing a fair six-sided dice until I roll a $3$. Let $X$ be the number of times I roll the dice. What is the value of $E[X]$?
So for this problem I was thinking that the answer would just be $1$. Here is my thought behind it.
For each turn there is a $1/6$ chance of hitting a three. If I keep rolling and rolling I will eventually hit a $3$. So the math works out to be $(1/6)*6$ which is equal to $1$. Does this logic make sense? I am a bit confused with how exactly I would go about picking the values for $P(X=x)$ and how to calculate expected value. Some insight would be very helpful.