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I'm stumped! Who can help. This is from a past test paper.
Let V and W be finite dimensional real vector spaces. Define the rank rT and nullity nT of a linear transformation T : V → W. State and prove the rank nullity theorem.
Let V1, V2, V3, V4 be finite dimensional spaces and Ti
maps.
Suppose that T1 is injective (one-to-one), T3 is surjective (onto), the image of T1 equals the kernel of T2 and the image of T2 equals the kernel of T3.
Show that (i) dim V2 = dim V1 + rT2 , (ii) dim V1 + dim V3 = dim V2 + dim V — Preceding unsigned comment added by 82.28.140.226 ( talk) 17:05, 29 May 2015 (UTC)
A gambler has an initial fortune of size k, where k is a non-negative integer. He plays a sequence of independent games such that on each play he wins 1 with probability p, or loses 1 with probability p, or his fortune remains unchanged with probability q, where 2p + q = 1. He decides to stop playing when either his fortune reduces to zero or his fortune reaches m, where m > k. Let N(k) be the number of games played until he stops.
How can I find EN(k)?
Now suppose, that his initial fortune is a random variable X, where X is binomially distributed with parameters m and α. What now is the expected number of games played? — Preceding unsigned comment added by 82.28.140.226 ( talk) 17:07, 29 May 2015 (UTC)
Mathematics desk | ||
---|---|---|
< May 28 | << Apr | May | Jun >> | May 30 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
I'm stumped! Who can help. This is from a past test paper.
Let V and W be finite dimensional real vector spaces. Define the rank rT and nullity nT of a linear transformation T : V → W. State and prove the rank nullity theorem.
Let V1, V2, V3, V4 be finite dimensional spaces and Ti
maps.
Suppose that T1 is injective (one-to-one), T3 is surjective (onto), the image of T1 equals the kernel of T2 and the image of T2 equals the kernel of T3.
Show that (i) dim V2 = dim V1 + rT2 , (ii) dim V1 + dim V3 = dim V2 + dim V — Preceding unsigned comment added by 82.28.140.226 ( talk) 17:05, 29 May 2015 (UTC)
A gambler has an initial fortune of size k, where k is a non-negative integer. He plays a sequence of independent games such that on each play he wins 1 with probability p, or loses 1 with probability p, or his fortune remains unchanged with probability q, where 2p + q = 1. He decides to stop playing when either his fortune reduces to zero or his fortune reaches m, where m > k. Let N(k) be the number of games played until he stops.
How can I find EN(k)?
Now suppose, that his initial fortune is a random variable X, where X is binomially distributed with parameters m and α. What now is the expected number of games played? — Preceding unsigned comment added by 82.28.140.226 ( talk) 17:07, 29 May 2015 (UTC)