Question

Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented...

Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented by random variable X and those of the second die be represented by random variable Y.

Let random variable Z be |X-Y|. The range of Z will be from 0 to 3.

1. Find E(Z).

2. Find P(Z = 1|Z <3).

3. What is the probability that you have to play the game 4 times before you roll Z=3?

4. What is the probability that when you play the game 10 times, you get Z=1 6 times out of the 10 rolls?

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Answer #1

Aus Possible outcomes - 16 which are (1, 1) (1,2), (1,3), 1114) (2, 1), (2.2),(2,3), (2,4) (3,1) (3,2), (3, 3), (3,4) (4,1),

1) So, 6/2) = {p (2 ) x 2 - 4 xo + 6x1+ 4 x 2 16 + 2 x3 16 16 20 1.25 POZZ 2) we need to find 243 P. (2011223) = P (2=1) + P

3) 3 Here P(2 is not equal to 3 theal which Jurther need to subhaut it by I 1 - 2 16 is played Ltd The gam so > 2/4 no Z :) p

P = (x=6) 6 locolo 10 To - 0.0348 which is the requered probability

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