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2. (D5) Let n = o(a) and assume that a =bk. Prove that <a >=<b> if...
1. Assume G=< a>. Let beg. Prove that o(b) is a factor of o(a)
1. Assume G=< a>. Let beg. Prove that o(b) is a factor of o(a)
2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
For all n E N prove that 0 <e- > < 2 k!“ (n + 1)!...
For all n E N prove that 0 <e- > < 2 k!“ (n + 1)! k=0 Hint: Think about Taylor approximations of the function e".
3. Let X be a geometric random variable with parameter p. Prove that P(X >k+r|X >...
3. Let X be a geometric random variable with parameter p. Prove that P(X >k+r|X > k) = P(X > r). This is called the memoryless property of the geometric random variable.
| Prove that for n e N, n > 0, we have 1 x 1!+ 2...
| Prove that for n e N, n > 0, we have 1 x 1!+ 2 x 2!+... tnx n! = (n + 1)! - 1.
.n= n(n-1)(n+1) for all n > 2. 12. Use induction to prove (1 : 2) +(2-3)+(3-4)...
.n= n(n-1)(n+1) for all n > 2. 12. Use induction to prove (1 : 2) +(2-3)+(3-4) +...+(n-1).n [9 points) 3
Let ne Nj. Prove that n < 2(6(n)).
Let ne Nj. Prove that n < 2(6(n)).
5. Prove that U(2") (n > 3) is not cyclic.
5. Prove that U(2") (n > 3) is not cyclic.
Help please! Let Be be Brownian motion and fix to > 0. Prove that By: =...
Help please!
Let Be be Brownian motion and fix to > 0. Prove that By: = Bto+t - Blo; t o is a Brownian motion.
Let →a=2→i−5→j−2→ka→=2i→-5j→-2k→ and →b=5→i−→kb→=5i→-k→. Find −→a+→b-a→+b→. Let ā = 27 – 53 – 2k and 7...
Let →a=2→i−5→j−2→ka→=2i→-5j→-2k→ and →b=5→i−→kb→=5i→-k→. Find
−→a+→b-a→+b→.
Let ā = 27 – 53 – 2k and 7 = 57 - K. Find - ã+ 7. <3i Х 5j k X>
1. Assume G=< a>. Let beg. Prove that o(b) is a factor of o(a)
2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
For all n E N prove that 0 <e- > < 2 k!“ (n + 1)! k=0 Hint: Think about Taylor approximations of the function e".
3. Let X be a geometric random variable with parameter p. Prove that P(X >k+r|X > k) = P(X > r). This is called the memoryless property of the geometric random variable.
| Prove that for n e N, n > 0, we have 1 x 1!+ 2 x 2!+... tnx n! = (n + 1)! - 1.
.n= n(n-1)(n+1) for all n > 2. 12. Use induction to prove (1 : 2) +(2-3)+(3-4) +...+(n-1).n [9 points) 3
Let ne Nj. Prove that n < 2(6(n)).
5. Prove that U(2") (n > 3) is not cyclic.
Help please!
Let Be be Brownian motion and fix to > 0. Prove that By: = Bto+t - Blo; t o is a Brownian motion.
Let →a=2→i−5→j−2→ka→=2i→-5j→-2k→ and →b=5→i−→kb→=5i→-k→. Find
−→a+→b-a→+b→.
Let ā = 27 – 53 – 2k and 7 = 57 - K. Find - ã+ 7. <3i Х 5j k X>
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