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southernpride9
03-21-2006, 07:18 PM
So here is my assignment:
A red die and a blue die are rolled together. Define X to be the max. of the two #'s rolled. For example, if the red die is 3 and the blue die is a 2 then X=3

1. Give the probability distribution table for the random variable X.

Possible combinations of the two die:
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

Maximum of two numbers rolled:
1 2 3 4 5 6
2 2 3 4 5 6
3 3 3 4 5 6
4 4 4 4 5 6
5 5 5 5 5 6
6 6 6 6 6 6

2. Compute E[X] and Var[X]

I know that X=1,2,3,4,5,6. But the formula for E[X] calls for:
E[X]=M sum of [x times p(x)] (not sure how to use these buttons in order to describe the symbols... lol). Anyway, I don't understand how to get the P(x). Can anyone help me?

edit: I have the student version of minitab, but I can't seem to find a way to do it on there... so if you know of anyway, I could work with that as well.

southernpride9
03-21-2006, 09:09 PM
So this is what I have came up with so far:
X P(X)
1 1/36=.027
2 2/36=.055
3 3/36=.083
4 4/36=.111
5 5/36=.138
6 6/36=.166

X * P(X) X squared X squared P(X)
.027 1 .027
.11 4 .44
.249 9 2.241
.444 16 7.104
.69 25 17.25
.996 36 35.856
2.516 (which is E(X) 42.938 (which is 19.980 squared)

My next question was-
3. Suppose the value of X is recorded for 5 rolls of the dice. Compute MuX bar
and the Standard Deviation X bar.
The formula for M Xbar is= the sum of X Bar P(Xbar)
The Area for SD is= SD 2/X Bar Squared.
So I came up with 2.52 for M X Bar
3.67 for SD X Bar.

Is this right so far?

jerryb
03-22-2006, 09:28 AM
You posted:

"So this is what I have came up with so far:
X P(X)
1 1/36=.027
2 2/36=.055
3 3/36=.083
4 4/36=.111
5 5/36=.138
6 6/36=.166"

which is a probability distribution, unfortunately its not correct for the problem. in your distribution the event "6" occurs with any of 11 outcomes of the trial. so that row of your distribution should be: 6 11/36 = .306

remeber that the total probability of all events MUST equal 1, so that will give you a check point if you total the probabilities and don't get 1 something is off.

cheers
jerry