Question: You simultaneously roll two fair dice until they show the sum of four or six. (a) What is the distribution of the number M,

You simultaneously roll two fair dice until they show the sum of

You simultaneously roll two fair dice until they show the sum of four or six. (a) What is the distribution of the number M, of throws? Give the relevant parameters. (b) What is the probability of ending with sum four? Now wait until the sum of the two dice is n times four or six, and denote by Nn the number of throws. (d) Determine the probability P[Nn, = kjfor all k N. (e) What is the distribution of the number M of throws with sum four up to Nn.

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