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# ST102 chi squared distribution question Watch talk to the uni Official Rep

1. 4. This is simply an exercise in using the definitions and tables of standard normal,
and t distributions.
The random variables are independent and identically distributed
as for i = 1, 2, 3. Find the following probabilities:

a. P( < 3)
b. P( < 5)
c. P( < 7)
d. P(> 2)

Part (a) I can do. Part (b) i'm having trouble with as the normal distribution is isn't a standard normal so i'm not sure how to use the distribution.

Many thanks
2. take square root on both sides and remember that it could be negative
3. (Original post by danny111)
take square root on both sides and remember that it could be negative
thanks . any ideas how i would use for part (c) and t distribution for part (d).
4. (Original post by JasdeepKochhar)
thanks . any ideas how i would use for part (c) and t distribution for part (d).
c) they are i.i.d. the normals. you know chi squared with n degrees of freedom is the sum of n standard normal squared. how can you rearrange the such that they are standard normal squared? is standard normal so you want to divide the by 4 (so divide by 4 on both sides) then they are square of standard normal. so together with i.i.d. this is with 3 DoF

d) really the same just use definition of t and not chi
5. (Original post by danny111)
c) they are i.i.d. the normals. you know chi squared with n degrees of freedom is the sum of n standard normal squared. how can you rearrange the such that they are standard normal squared? is standard normal so you want to divide the by 4 (so divide by 4 on both sides) then they are square of standard normal. so together with i.i.d. this is with 3 DoF

d) really the same just use definition of t and not chi
Thanks SO much
6. so together with i.i.d. this is with 3 DoF

[/QUOTE]

Can you please explain to me in detail, please ? for part c and d.
I still don't understand, how you derive chi^2 with 3 DoF. How do you know is 3 DoF ?
7. Can you please explain to me in detail, please ? for part c and d.
I still don't understand, how you derive chi^2 with 3 DoF. How do you know is 3 DoF ?
If you watch the first 10 minutes or so of the Review Session on Jan 27th, James goes through some of these basic results

Updated: April 28, 2011
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