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I was trying to solve problem no 1 and 2 of section 3.4 of the book "Principal of applied mathematics" by James P Kenner.
But i am stuck with that. Can anyone help me?
http://books.google.com/books?id=YxL_Z650nNoC&dq=principle+of+applied+mathematics,+keener&printsec=frontcover&source=bl&ots=jshM01BmsL&sig=WnuYEUAhojbUdfBlQSZshVBkWOo&hl=en&ei=mqXiStHrD5Wn8AaCrKDpAQ&sa=X&oi=book_result&ct=result&resnum=3&ved=0CBEQ6AEwAg#v=onepage&q=&f=false
The problems are here at page no 130.
1. Let X denote the mean of a random sample of size 75 from the distribution that has the pdf f (x)1, 0 x<=1. Calculate P (0.45 <X< 0.55).
2. Derive the moment-generating function for the normal density.
3. Let Y n (or Y for simplicity) be b (n, p). Thus, Y / n is approximately N [p, p (1 p) / n]. Statisticians often look for functions of statistics whose variances do not depend upon the parameter. Can you find a function, say u(Y / n), whose variance is essentially free of p?
can anyone help me with these problems?
1) Z is a normal subgroup of R(real number under addition.).Show that the quotient group R/Z is isomorphic to the circle group K.
2) Prove that every quotient group of a cyclic group is cyclic.
3) Let H is a normal subgroup of a group G. Show that the order of aH as an element of the quotient group G/H divides the order of a єG.
can anyone help me doing these?
Definition: when H, K are subgroups of G, we define HK to be the set of all elements of G that can be written in the form hk where h is in H and k is in K.
1) let H be a subgroup of a group G and N be a normal subgroup of G.show that HN is a subgroup of G and N be a normal subgroup of HN.
2) let H,K and N be a subgroup of a group G, K is normal subgroup of H and N is normal subgroup of G.prove that NK is normal subgroup of NH.
3) let H1 and H2 be subgroups of a group G and N1 subgroup of H1 and N2 subgroup of H2.then show that
N1(H1 intersection N2) is normal subgroup of N1(H1 intersection H2)
and (H1 intersection N2)(H2 intersection N1) normal subgroup of (H1 intersection H2)
can u help me of these 3 proofs?
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i have wrote intersection,normal group literary rather than using sign.H1,H2,..........Hn
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