A fair die is rolled twice, with outcomes X for the first roll and Y for the second roll. Find the moment generating function MX`Y ptq of X ` Y . Note that your answer should be a function of t and can contain unsimplified finite sums.

Step-by-step explanation:

The objective is to find the moment generating  function of  .

We are being informed that the fair die is rolled twice;

So; X to be the value for the  first roll

Y to be the value of the second roll

The outcomes  of X are:  X = {1,2,3,4,5,6}

Where ;

The outcomes  of Y are:  y = {1,2,3,4,5,6}

Where ;

The outcome of Z = X+Y

= [2,3,4,5,6,7,8,9,10,11,12]

Here;

∴ the moment generating function is as follows:

=

⇒

=

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.