Question 1193219: I have done i,ii,iii just need v but unsure if right
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.
iv) Draw a vertical line graph to illustrate the probability distribution of 𝑋(with probability on the y-axis and 𝑋- values on the x-axis) and describe the shape of the distribution. (You may use excel or simply draw by hand on paper)
v) Evaluate the following. You must show your working (you may use Excel where possible to show working)
1. 𝑃(𝑋>8)
2. 𝑃(|𝑋−7|<3)
3. 𝐸(𝑋)
4. 𝑉𝑎𝑟(𝑋)
A.i)
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
ii. X 1 2 3 4 5 6
P(X=x) 1/36 3/36 5/36 7/36 9/36 11/36
P(x) 1/36 4/36 9/36 16/36 25/36 1
iii.
P(X=x) {1/36 x = 1
3/36 x = 2
5/36 x = 3
7/36 x = 4
9/36 x = 5
11/36 x = 6. this right ??
v. is here but unsure if is right
7 8 9 10 11 12
v. 13/36 15/36 17/36 19/36 21/36 23/36
1 𝑃(𝑋>8) = P ( X≥9) F(9) =2.25 49/36=1.36 64/36=1.78 81/36=2.25 100/36=2.78 121/36=3.36 144/36=4
2 𝑃(|𝑋−7|<3)
3 𝐸(𝑋)= 10.63 x p(x) xp(x) x^2 p(x) (x-m)^2P(X)
or 4.472 1 0.027 0.27 0.03
4 Var(x) =71.001216 2 0.11 0.22 0.44
1^2=1 3 0.25 0.75 2.25
2^2=4 4 0.44 1.76 7.04
3^2=9 5 0.69 3.45 17.25
4^2=16 6 1 6 36
5^2=25 ∑p(x)=2.52 ∑xp(x)=10.63 ∑x^2p(x) = 63.01
6^2=36
91-4.472^2
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website! .
Hey, I looked at your post, and I see that parts (ii) and (iii) are solved incorrectly.
I think that you don't know relevant theory.
From the other side, I see your intention to do the job on your own, which I like very much.
So, my advise to you is to read a lesson
- Rolling a pair of fair dice
in this site. You will find there many other similar solved problems.
After reading it, you will be able to solve the mentioned parts in a correct way, I believe.
When you redo and complete the parts (ii) and (iii) on your own, you may re-post your solution to this forum (to me) for checking.
///////////////
David, I got your comment.
Your error in parts (ii) and (iii) is that you consider X as a variable for single separate throw,
while the problem DEFINES X as the sum of values, when a pair of dice is thrown.
So, do not argue with me . . . // If your desire to argue with me prevails your desire to learn, then you are not my customer . . .
You better READ the lesson which I recommended you.
It is written SPECIALLY for those individuals who care about developing their mind, their skills and their knowledge.
I will be glad to contact with you later, when I see your progress.
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