Q1 (10 points). For each scenario below, describe what distribution the random variable X follows. Write down the name of the distribution, the distribution function, and the values that X takes (for example: X ~ B (0.5), 𝑝(𝑥) = 0.5!0.5"#!, 𝑥 = 0, 1).
(1) Draw ten cards from a deck of cards with replacement. Define X as the number of diamond cards that were drawn.
(2) Draw cards from a deck of cards with replacement until drawing a diamond card. Define X as the number of draws.
(3) Draw one card from a deck of card. Define X = 1 if the card is diamond, X=0 otherwise.
(4) Draw cards from a deck of cards with replacement until drawing sixth diamond card. Define X as the number of draws.
Draw ten cards from a deck of cards without replacement. Define X as the number of diamond cards that were drawn.