Question 1193374: I have done I but need help on ii,iii,v. I need help xx
The random variable 𝑋 is given by the sum of the scores when two ordinary dice are thrown. For this experiment:
i) Write down the sample space 𝑆.
ii) Draw a table to show the probability distribution and the cumulative
distribution of 𝑋.
iii) Write down the probability function of 𝑋.
v) Evaluate the following. You must show your working
1. 𝑃(𝑋>8)
2. 𝑃(|𝑋−7|<3)
3. 𝐸(𝑋)
4. 𝑉𝑎𝑟(𝑋)
Dices 1 2 3 4 5 6
1 1,1 1,2 1,3 1,4 1,5 1,6
2 2,1 2,2 2,3 2,4 2,5 2,6
3 3,1 3,2 3,3 3,4 3,5 3,6
4 4,1 4,2 4,3 4,4 4,5 4,6
5 5,1 5,2 5,3 5,4 5,5 5,6
6 6,1 6,2 6,3 6,4 6,5 6,6 sample space = 36
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! the probability distribution is
for 2 as a sum 1/36 and |x-7| is not <3
3--2/36
4--3/36
5--4/36 and |x-7| IS <3, as are the next 4
6-5/36
7-6/36
8-5/36
9-4/36
10-3/36
11-2/36
12-1/36
So >8 would be 10/36 (may reduce or use decimals)
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|x-7| < 3 would be the 5-9 group, the sum of which is 2/3
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E(x)=7
V(x)=sum of squared deviations:
pair 2/12 and 3/11 and 4/10 and 5/9 and 6/8, and 7 will contribute nothing.
25*(2/36)+16(4/36)+9(6/36)+4(8/36)+1(10/36)=(1/36)(210)=210/36=5.833
(singular die, plural dice)
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