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# Short S1 Question.....Help! Watch

1. A fair dice is thrown once and the random variable X represents the value on the uppermost face:

a) Find the mean and variance of X
b) Calculate the probability that X is within one standard deviation of the mean

a)

E(X) = n+1/2 = (6+1)/2 = 7/2 = 3.5

Var(X) = (n+1)(n-1)/12 = (6+1)(6-1)/12 = 35/12 = 2.92 (3 s.f.)

b)

Mean - 1 standard deviation:

3.5 - (35/12) = 0.583

Mean + 1 standard deviation:

3.5 + (35/12) = 6.42

Probability of it being in this range:

=P(0.583.......<R< 6.42) = P(1 =/< R =/< 6)

How do I find the probability? Help please!
2. (Original post by Mambo No. 5)
A fair dice is thrown once and the random variable X represents the value on the uppermost face:

a) Find the mean and variance of X
b) Calculate the probability that X is within one standard deviation of the mean

a)

E(X) = n+1/2 = (6+1)/2 = 7/2 = 3.5

Var(X) = (n+1)(n-1)/12 = (6+1)(6-1)/12 = 35/12 = 2.92 (3 s.f.)

b)

Mean - 1 standard deviation:

3.5 - (35/12) = 0.583

Mean + 1 standard deviation:

3.5 + (35/12) = 6.42

Probability of it being in this range:

=P(0.583.......<R< 6.42) = P(1 =/< R =/< 6)

How do I find the probability? Help please!
You may want to check you're calculation of the S.D. again...
Try using: Var(X) = E[X^2] - [(E[X])^2]
3. (Original post by XShmalX)
Is it not just 1 as R could be 1,2,3,4,5 or 6?
The answer in the book is 2/3 . Any ideas?
4. (Original post by XShmalX)
Is it not just 1 as R could be 1,2,3,4,5 or 6?
My variance calculation is right, the book's answers confirm it.
5. (Original post by Mambo No. 5)
My variance calculation is right, the book's answers confirm it.
But you need to square root it to get the standard deviation so S.D=1.7018... which gives a smaller range of values.
ie. 2-5 so P=4/5=2/3
6. (Original post by XShmalX)
But you need to square root it to get the standard deviation so S.D=1.7018... which gives a smaller range of values.
ie. 2-5 so P=4/5=2/3
Thank You. +1rep
7. (Original post by Mambo No. 5)
Thank You. +1rep
Thanks! You're most welcome!
8. Sorry I still don't get the b part.

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Updated: December 26, 2013
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