Q$1)$ Let's roll a fair die repeatedly until a number less than $3$ is observed. If $x$ is the total number of times we roll the die,

a$)$ Which distribution is $x$ random variable?

b$)$ Find $P(x=x),$ for $x=1,2,3,$dots

c$)$ Find the probability that a number less than $3$ is observed in the $6$ th rolls.