Two balanced dice are rolled. Let X be the sum of the two dice.(i) Obtain the probability distribution of X (i. e. what are the possible values for X and the probability for obtaining each value?). Check that the probabilities sum to one.(ii) What is the probability for obtaining X >= 8?(iii) What is the average value of X?

i) X       2       3       4         5        6       7        8        9       10      11

P(X) 1/36   2/36  3/36  4/36  5/36  6/36  5/36  4/36  3/26  2/36

X       12

P(X)  1/36

And if we check for this case when we add the probabilities we got:

ii)

iii)Explanation:

For this case we can define the following sample space for a two balanced dice:

(1,1) (1,2) (1,3) (1.4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

We have a total of 36 possible pairs

Part a

(i) Obtain the probability distribution of X (i.e. what are the possible values for X and the probability for obtaining each value?).

And the possible values ofr X on this case are : X = 2,3,4,5,6,7,8,9,10,11,12

Now we can obtain the porbability distribution for X like this:

X       2       3       4         5        6       7        8        9       10      11

P(X) 1/36   2/36  3/36  4/36  5/36  6/36  5/36  4/36  3/26  2/36

X       12

P(X)  1/36

And if we check for this case when we add the probabilities we got:

(ii) What is the probability for obtaining X >= 8?

For this case we want this probability:And if we replace we got:

(iii) What is the average value of X?

For this case we can use the definition of expected value like this and we got:

And if we replace we have:

answer: the direction of the wind is expressed as the direction from which the wind is blowing. for example, easterly winds blow from east to west, while westerly winds blow from west to east.

explanation:

seeing the graph would