Statistics Homework Help!

Question

Question is: let the random variable x represent the sum of the points in two tosses of a die.

 

A) list the possible values of x

 

B) For each value of x, list the corresponding elementary outcomes.

 

C) obtain the probability distribution of x 

Answer 1

Using a 6-sided die:

 

A) Possible values of 'x' include:  2 <= x <= 12 (where <= is less than, or equal to, in the range of values) 

 

B) Based on the following, elem. outcomes for 5 <= x <= 11 can also be determined:

 

     For x = 2, elem. outcomes are (1,1)
     For x = 3, elem. outcomes are (1,2) and (2,1)
     For x = 4, elem. outcomes are (1,3), (2,2), and (3,1)
     ...

     ... 

     ...

     ...

     ... 

     ... 

     ...

     For x = 12, elem. outcomes are (6,6)

 

C) The probability distribution will depend on your calculations for the random probabilities of rolling a particular value of 'x' in relation to total possibilities (the SUM of all elem. outcomes for 2 <= x <= 12). 

 

For example, there is only ONE possible elem. outcome (1,1) for a pt. total of 2 (when x=2), TWO possible elem. outcomes for a pt. total of 3 (when x=3), THREE possible elem. outcomes for a pt. total of 4 (when x=4), etc. - BASED ON part B), above.

 

GOOD LUCK !