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Central Limit Theorem (normal distributions) (1 Viewer)

leehuan

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I think this question may be asking me to construct a proof so I don't want to quote the CLT or anything



Previously proven:



 

leehuan

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Funnily enough part c was this (I haven't attempted it yet.)



But I guess this is the CLT part.
___________

And edit: Yep ok!
 

InteGrand

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Funnily enough part c was this (I haven't attempted it yet.)



But I guess this is the CLT part.
This isn't CLT either. It's simply induction using previous results (similar to the Bonferoni's Inequality induction method I mentioned in another thread if you remember it).
 

leehuan

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This was the other one I had trouble on for the time being (please)

 

Trebla

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This question is quite advanced for first year level lol
 

leehuan

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This question is quite advanced for first year level lol
Yeah a fair few of my algebra/probability questions get marked with an [H] but I still try them anyway, or want to see how they're done
 

mreditor16

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Yeah a fair few of my algebra/probability questions get marked with an [H] but I still try them anyway, or want to see how they're done
As you will see when you start MATH1151 past papers, there will be minimal questions of [H] difficulty level in your final exam. So don't be dishheartened if nearly all of the [H] questions are close to impossible to do when you're going through tutorial hw.
 

integral95

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hehe if you plan to do 2nd year stats, then some of these materials are useful, otherwise you're kind of wasting your time
 

seanieg89

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hehe if you plan to do 2nd year stats, then some of these materials are useful, otherwise you're kind of wasting your time
No way, that's such a negative mindset. Even if you don't do a followup subject, pushing yourself beyond the minimum effort required in a maths/stats subject and doing the more difficult problems will definitely sharpen your general problem solving chops. The more difficult things you get exposed to and bang your head against, the better.
 

leehuan

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As you will see when you start MATH1151 past papers, there will be minimal questions of [H] difficulty level in your final exam. So don't be dishheartened if nearly all of the [H] questions are close to impossible to do when you're going through tutorial hw.
Yeah I realised. Did a past paper and it wasn't the worst (though I did have trouble with wording and it took me like the whole day to get through the paper lol)
Just gotta make sure I know the required stuff.
hehe if you plan to do 2nd year stats, then some of these materials are useful, otherwise you're kind of wasting your time
Pure maths major makes me pick a second year stats course
No way, that's such a negative mindset. Even if you don't do a followup subject, pushing yourself beyond the minimum effort required in a maths/stats subject and doing the more difficult problems will definitely sharpen your general problem solving chops. The more difficult things you get exposed to and bang your head against, the better.
Yeah. I get sad over it when I don't get it but I always do it anyway because I want to progress further in my maths life than most of my peers at least lol.

Half of them come to tutorials, I tell the tutor what qns to do, then they just copy the method down as if they never did the qn before
 

leehuan

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Is this what I'm basically supposed to do (we're approximating binomial distributions)





I used the table UNSW provided for standard normal probabilities
 

InteGrand

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Yeah that's basically what needs to be done. Although, it might be better to find Pr((100/150) < X-bar ≤ 1) instead, since X-bar can't exceed 1, but if you use the Normal approximation, you make it as though it can exceed 1, so you need to account for that by making sure you compute Pr((100/150) < X-bar ≤ 1). It'll make completely negligible numerical difference though actually in this case, so you don't need to really worry about it.
 
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leehuan

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Yeah that's basically what needs to be done. Although, it might be better to find Pr((100/150) < X-bar ≤ 1) instead, since X-bar can't exceed 1, but if you use the Normal approximation, you make it as though it can exceed 1, so you need to account for that by making sure you compute Pr((100/150) < X-bar ≤ 1). It'll make completely negligible numerical difference though actually in this case, so you don't need to really worry about it.
When X-bar = 1 I get Z=10. Lol yeah I guess it's a minute difference
 

InteGrand

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When X-bar = 1 I get Z=10. Lol yeah I guess it's a minute difference
Yeah the chance of having a normal r.v. be 10 standard deviations away from its mean is basically 0, so it makes no real difference.
 

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