Question

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. (2.5 points) Find E(Z). 2. (2.5 points) Find P(Z = 21Z >1). 3. (2.5 points) What is the probability that you have to play the game 6 times before you roll Z=3? 4.(2.5 points) What is the probability that when you play the game 10 times, you get Z=05 times out of the 10 rolls?

Answer 1

Pg Nor Answert 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. The sample space for rolling two 4 sided dice contains 16 possible outcomes. (1, 1), (1,2), (1,3), (1,4) (2,1), (2,2), (2,3), (2,4) (3,1), (3,2), (3,3), (3,4) (4,1),(4,2),(4,3),(4,4). the possible values of 2= |x-1) and their frequencies. 3 4 6 4 9 > 16 16 P(2=0) - P(2-1) = PC 2-2) and P(Z =3) = ③ E (2) can be considered as below: E(2) = {P(2) x2 4 / 3 x + 1/4 x 1 + 4 × 2 + 1/48 x 3. 20 - 1.25 1. E(2) -1.25 ܝܘ OP(Z = 2/2>1) can be considered can be considered as below: P(2-2/2 >1). P(2=2) Prasil

2 P(2=2) P(2-2) +P(2=3) 4/16 4/16+16 = 1 / 2 P(2=2/2>1)= ? ♡ The probability that you have to play the game 6 times before you roll Z=3. P(2 not equal to 3) = 1-1/16 --thus, required Aobability = fent 3 14 6 2 16 - 10 orol the game to This the probability that when you play times you get 2=0.5 times out of the 10 rolls. Here, can be solved by using bromial distribution. let x denote the no. of times you get z=0. Here, n=10, P(x= 6) = (# Docentes - 10.0584) P=4 To InP 12 16 loch