Homework Answers
Exercise 6.14 Let y be distributed Bernoulli P(y = 1) unknown 0<p<1 p and P(y =...
Exercise 6.14 Let y be distributed Bernoulli P(y = 1) unknown 0<p<1 p and P(y = 0) = 1-p f or Some (a) Show that p E( (b) Write down the natural moment estimator p of . (c) Find var (p) (d) Find the asymptotic distribution of vn (-p) as no. as n> OO.
2. Let YBinomial (n, p) where p docs not depend on . Without using the WLLN...
2. Let YBinomial (n, p) where p docs not depend on . Without using the WLLN (but you can use e.g. Chebychev's inequality) show that (a) Y/n-, p as n → oo (b) (1-Y/n)-> (1-p) as n → oo
IF Let x(t) Show that e 20" σ>0, and let (o) be the Fourier transform of...
IF Let x(t) Show that e 20" σ>0, and let (o) be the Fourier transform of x(t) .
Extra Credit Question:[4+4=8 pts) If E [exp(aX)] exists for a given constant a, then show that...
Extra Credit Question:[4+4=8 pts) If E [exp(aX)] exists for a given constant a, then show that for to (a) exp(-at)P(x >t) <E (exp(aX)], if a > 0. (b) exp(-at)P(X <t) <E (exp(aX)], if a < 0.
b. Let U2 u~xã. Show that E(b)=n-2 for n > 2. LU
b. Let U2 u~xã. Show that E(b)=n-2 for n > 2. LU
7.(15) Let PALINDROMEDFA = { <M> Mis a DFA, and for all s E L(M), s...
7.(15) Let PALINDROMEDFA = { <M> Mis a DFA, and for all s E L(M), s is a palindrome } Show that PALINDROMEDFA E P by providing an algorithm for it that runs in polynomial time.
n. 7. Let Xi, , Xn be iid ;0) =-e-r2/0 where x > 0. Sho w...
n. 7. Let Xi, , Xn be iid ;0) =-e-r2/0 where x > 0. Sho w that θ=「x? is based on f (x efficient.
Let a1 = 3 and an+1 = a + 5 2an for all n > 1...
Let a1 = 3 and an+1 = a + 5 2an for all n > 1 Prove that (an)nen converges and find limn7oo an:
which of these answers is correct? NUMBER 1 NUMBER 2 also please give the reason. Thank...
which of these answers is correct?
NUMBER 1
NUMBER 2
also please give the reason.
Thank you!
Construct a context-free grammar for the language L={ ab'ab'an> 1}. S → AAa A → aB B → 6B|bb S->ata T-> bCb C->bCba
1. Recall the following theorem. Theorem 1. Let a, b, m,n e N, m, n >...
1. Recall the following theorem. Theorem 1. Let a, b, m,n e N, m, n > 0 and ged(m,n) = 1. There erists a unique r e Zmn such that the following holds. x = a (mod m) x = b (mod n) please show that such solution is unique.
Exercise 6.14 Let y be distributed Bernoulli P(y = 1) unknown 0<p<1 p and P(y = 0) = 1-p f or Some (a) Show that p E( (b) Write down the natural moment estimator p of . (c) Find var (p) (d) Find the asymptotic distribution of vn (-p) as no. as n> OO.
2. Let YBinomial (n, p) where p docs not depend on . Without using the WLLN (but you can use e.g. Chebychev's inequality) show that (a) Y/n-, p as n → oo (b) (1-Y/n)-> (1-p) as n → oo
IF Let x(t) Show that e 20" σ>0, and let (o) be the Fourier transform of x(t) .
Extra Credit Question:[4+4=8 pts) If E [exp(aX)] exists for a given constant a, then show that for to (a) exp(-at)P(x >t) <E (exp(aX)], if a > 0. (b) exp(-at)P(X <t) <E (exp(aX)], if a < 0.
b. Let U2 u~xã. Show that E(b)=n-2 for n > 2. LU
7.(15) Let PALINDROMEDFA = { <M> Mis a DFA, and for all s E L(M), s is a palindrome } Show that PALINDROMEDFA E P by providing an algorithm for it that runs in polynomial time.
n. 7. Let Xi, , Xn be iid ;0) =-e-r2/0 where x > 0. Sho w that θ=「x? is based on f (x efficient.
Let a1 = 3 and an+1 = a + 5 2an for all n > 1 Prove that (an)nen converges and find limn7oo an:
which of these answers is correct?
NUMBER 1
NUMBER 2
also please give the reason.
Thank you!
Construct a context-free grammar for the language L={ ab'ab'an> 1}. S → AAa A → aB B → 6B|bb S->ata T-> bCb C->bCba
1. Recall the following theorem. Theorem 1. Let a, b, m,n e N, m, n > 0 and ged(m,n) = 1. There erists a unique r e Zmn such that the following holds. x = a (mod m) x = b (mod n) please show that such solution is unique.
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