Question 1087494: I'm having issues trying to get this problem down pact, I dont know what im doing wrong. I have tried multiple times not getting the answer.
Dice. The random variable Y is the sum of the dice when two balanced dice are rolled. Its
probability distribution is as follows:
y 2 3 4 5 6 7 8 9 10 11 12
P(Y = y) 3 6
4
3 6
3
3 6
2
3 6
1
3 6
1
3 6
8
3 6
1
9
1
1 2
1
3 6
6
1 2
1
a. Find and interpret the mean of the random variable
b. Find the standard deviation of the random variable
c. Draw the probability histogram of the random variable.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The above isn't clear, but I will give you the distribution for all 11 possibilities
2 is 1/36, product 2/36
3 is 2/36,product is 6/36
4 is 3/36, product is 12/36
5 is 4/36, product is 20/36
6 is 5/36, product is 30/36
7 is 6/36, product is 42/36
8 is 5/36, product is 40/36
9 is 4/36, product is 1
10 is 3/36, product is 30/36
11 is 2/36, product is 22/36
12 is 1/36, product is 12/36
sum of x*p(x) is expected value and is 252/36 or 7, which is the most common roll, and in a symmetrical mass function, the unique middle should be the expected value.
variance is sum of squares of the difference * probability
for 2, 25*1/36 or 25/36
for 3, 16*2/36 or 32/36
for 4, 9*3/36=27/36
for 5, 4*4/36=16/36
for 6, 1*5/36=5/36
for 7,0
for 8, 1*5/36=5/36
for 9,4*4/36=16/36
for 10,9*3/36=27/36
for 11,16*2/36=32/36
for 12, 25*1/36=25/36
sum is 210/36=5.8333
sqrt of that is sd=2.42
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