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Math Help - distrubition type

  1. #1
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    distrubition type

    Hello. There are two questions here that I really have no idea what to do.
    I scanned the 2 questions since I am awful with the online math code.



    I cant figure out where to start. If someone can just help me with one of them, then I can attempt the rest. Thank you
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  2. #2
    MHF Contributor matheagle's Avatar
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    I cannot read that scan.
    I bet I can answer your questions if you would retype it for me.
    It looked like a linear combination of normals and also squares of normals, creating Chi-Square rvs.
    If so, that should be rather easy.
    There might be some t and F's in there too.

    --------------------------------------------------------------------------------

    I blew it up and I had to laugh.
    I'm teaching out of Wackerly (I also knew Dennis when I was at Florida)
    this semester and I just assigned those two problems this year.
    I even have the sol manual, but thats not necessary

    37a each Y_i is a N(0,1)
    so the square is a Chi-square with one df
    the sum of indep chi-squares is a chi-square with the df each to the sum
    of those df so the answer is chi-square with 5 dfs

    37b U divided by sigma squared is a chi-square w n-1=4 df
    but since sigma=1 here we don't need to see sigma.
    Hence we have a chi-square w 4 dfs.

    37b Thats U (from part b) plus an indep chi-square w 1 df
    hence it's a chi-square w 5 df (add the dfs)

    38a that's a t with 5 dfs, because its a standard normal divided
    by a chi-square divided by its dfs and square rooted

    38b that's a t with 4 dfs, for the same reason as in (a), just take
    the 2 and rewrite him as square root of 4 and place him under the denominator inside a square root.

    38c thats an F with 2 and 4 dfs, because you can write him as a chi-square (with 2 df)divided by two OVER a chi-square (with 4 dfs) divided by 4.
    Last edited by mr fantastic; February 22nd 2009 at 02:09 AM. Reason: Merged posts
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