Could Someone Please Help Me Solve This Statistics Problem?

Question

The Question: For this assignment, you will create and use a probability distribution that reflects rolling a pair of dice. First, construct a probability distribution for rolling 5's, displaying it as a table. Be sure to include a column for x and a column for P(x). Next, use the P(x) values to calculate the mean, standard deviation, and variance for x (Remember...x = number of fives rolled when two fair dice are tossed at the same time not a total of 5!).

I have determined that the probabilities of getting 5's when rolling a pair of dice is 0, 1, and 2, seeing as you the possibilities can either be that you roll zero 5's, you roll one 5, or you roll two 5's. I just need help calculating the probabilities.

The table should look similar to below:

x P(x)

------------------

0 ?

1 ?

2 ?

Answer 1

Probability of 2 fives out of two dice roles is 1/36 (1 possibility out of 6² possible rolls

Probability of one 5 out of two dice is 11/36 1,2,3,4,6 - 5 twice ( because 1 on die 1 and 2 on die 22 is matched be 1 on die 2 and 2 on die 1) 10/36

Probability of no 5's is 1-11/36 or 5/6*5/6 = 25/36

The average is the sum of number of 5's times the probability of that number of 5's

(Expected value of number of 5's or mean value)

Variance: Calculate the sum of the number of 5's squared times the probability of 5's (Sum of x²P(x)

Take the sum of the x²P(x) and subtract the mean squared.

S.D = sqrt(Var)

Please consider a tutor. Take care