1 Consider the experiment of rolling two identical fair 4sid

1. Consider the experiment of rolling two identical fair 4-sided dice. The sample space of this experiment consists of 16 ordered pairs of numbers, all equally likely. (If it helps, imagine that o other is green.) Define a random variable X to be the difference (i.e. subtraction smaller face values on a single roll of the two dice. a. What is the domain D of this rv? ne die is red and the ) between the larger and [5 points] 3 b. For each value x E D let A, be the set of outcomes in the sample space s that correspond to (i.e result in) the value X-x. List all of the events and verify thathey are pairwise-disjoint and their union is the entire sample space 17 points] c. Give the probability mass function (pmf) for X. Use fractions or decimals to 4 places. 6 points) p(x)

Solution

sol)

Since 4faced 2 dice are rolled then total cases are 16

a) Let X be the difference between larger and smaller values

then the domail is {3,2,1}

c)

x 3 2 1

p(x) 1/6 2/6 3/6

d) E(x) =3*(1/6)+2*(2/6)+1*(3/6) = 5/3

e) varaince =3²*(1/6)+2²*(2/6)+1²*(3/6) - (5/3)^{2 =} 5/9