i am currently working on a study guide and one of the questions i am completely stuck on and have no idea how to do it.
Question is.
You are interested in the number of rolls of a fair $6$ sided die until a number $2$
shows up.
Let $X =$ The number of times you roll the die until a number $2$ shows up.
(a) What type of random variable is $X$?
(b) How many rolls do you expect it to take? That is, what is the expected value, or mean, of the random variable $X$?
(c) What is the probability you roll a $2$ for the first time on the fourth roll? i.e. What is $P(X = 4)$?
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