Solve Question 1,2,3,8,10

HW2 Stat 4201 Due Date: 9/13/2021 As a reminder, please submit the homework as one single pdf le in the Carmen dropbox provided. Question 1 Suppose two fair 4-sided dice, each numbered {1, 2,3,4} are rolled. a) Dene the sample space S. b) Find the distribution of M, where M is the minimum of the two dice. c) Find the probability that M is equal to 2 or 3. Question 2 Suppose A and B are events such that P[A) = 0.5 and P(B) = 0.8. Without making any other assumptions, prove that 0.3 S P(A ['1 B) S 0.5. Question 3 Consider three events. Let A be the event that a household subscribes to Netix. Let B be the event that a household subscribes to Hulu. Let C be the event that a household subscribes to cable. 30% of households only subscribe to cable, while 10% only subscribe to Netix and 15% only to Hulu. 10% don't subscribe to any service, while 20% subscribe to all three services. a) What is the probability that a random customer will subscribe to exactly two services? b) Let P{A ['1 B) = P(B ['1 C) = P(A F] C). What is P(A)? (HINT: What areas are included in (A D B) on your Venn diagram? If P[A FIB) = P(B DC) = P(AC) what must P(AB ['1 C\") be?) c) Find P(C\"|A) Question 4 Do exercise 2.70 from the text. Question 5 Do exercise 2.80 from the text. Question 6 Do exercise 2.112 from the text. [Note the question is somewhat poorly worded. If a student sees a card that says \"I smoke . . .\" they answer yes if they smoke and no if they don't. If they see the other card, they say yes if they don't smoke and no if they do. Question 7 Do exercise 3.4 from the text. Question 8 Let S be the sample space corresponding to three tosses of a fair coin. Give a verbal description of the following events: a) A = {HHH, HHT, HTH,HTT}; b) B = {HHH,HHT,HTH,THH}; c) Show that A and B are not independent. Question 9 Do exercise 3.22 from the text. Question 10 Suppose that the random variable X has a density given by c x sin[x) for 0