We have two fair three-sided dice, indexed by =1,2 . each die has sides labelled 1 , 2 , and 3 . we roll the two dice independently, one roll for each die. for =1,2 , let the random variable represent the result of the th die, so that is uniformly distributed over the set {1,2,3} . define =− . calculate the numerical values of following probabilities, as well as the expected value and variance of : (a) p(x = 0) = (b) p(x = 1) = (c) p(x = −2) = (d) p(x = 3) = 2. let y = x2 . calculate the following probabilities: (a) p(y = 0) = (b) p(y = 1) = (c) p(y = 2) =

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

true

step-by-step explanation:

the answer would be c:   ax + b = ax + c

step-by-step explanation:

2x + 8

step-by-step explanation: