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Probability
Hiya!
I'm having quite a bit of trouble with these few.
1. Show that if F and G are sigma field, then FnG is also a sigma field, but in general FuG is not.
2. Let X be a rv, and let g:R->[0,inf] be an increasing function such that
E(g(x))<inf. Show that for any real a, one has:
P(X>a)<<E(g(x))/g(a).
In particular P(X<a)<<E(exp{b(X-a)}) for any real a, and any b>0.
3. P(X_n=k)=nCkp^k(1-p)^(n-k)
a) What is the moment generating function of X_n?
b) Let p=P_n ->0 as n tends to infinity in such a way that n.p_n -> b>0. Show that as n tends to infinity, Mx_n (t) tends to exp{b(e^t-1)}
Please could you show me at least where to look for how to work these out? I really dont have many resources here.
Thanks in advance i'm really stuck.
I'm having quite a bit of trouble with these few.
1. Show that if F and G are sigma field, then FnG is also a sigma field, but in general FuG is not.
2. Let X be a rv, and let g:R->[0,inf] be an increasing function such that
E(g(x))<inf. Show that for any real a, one has:
P(X>a)<<E(g(x))/g(a).
In particular P(X<a)<<E(exp{b(X-a)}) for any real a, and any b>0.
3. P(X_n=k)=nCkp^k(1-p)^(n-k)
a) What is the moment generating function of X_n?
b) Let p=P_n ->0 as n tends to infinity in such a way that n.p_n -> b>0. Show that as n tends to infinity, Mx_n (t) tends to exp{b(e^t-1)}
Please could you show me at least where to look for how to work these out? I really dont have many resources here.
Thanks in advance i'm really stuck.
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