Recent content by Beowulf2007

Hi Then limit must be \mathop{\lim} \limits_{t \to \infty} te^{-t^2} = 0, then assuming this is true then f(x1) an f(x2) then tend to the same limit since f is continious (by the mvt), and therefore the integral f(t) -> 0, then t tends to infinity? q.e.d. Cheers, Beowulf and thanks your...

Homework Statement Given the integral f(t) = \int_{t}^{2t} e^{-x^2} dx How do I then prove that f(t) = 0 if t tends to infinity? Homework Equations The Attempt at a Solution I can that if I make t goes from minus infinity to zero, then the limit will tend to 1, but when...

So the that for any epsilon, if n is arbitrary larger then Beta_n will stay small and will therefore tend to zero? And that is simply the proof? BR Beowulf

Just so we understand each other. Do You mean? T \subseteq U and U \subseteq T Therefore their union is defined as T \cup U = T + U Therefore their intersection is defined as T \cap U = T \cdot U And then use this fact to claim that my result in (1) and (2) are true! How...

Regarding (1) do I considered the events to the mutually exclusive?? And therefor if P(T) occurs then P(U) also occurs and thus P(T u U ) = P(T) + P(U)? Or is the explanation more simple?? In (2) Is it something to do with the events being mutually inclusive?? SR Beowolf

Hi an Thank You for Your reply. I can see if I make n large then epsilon will have to be very small. Is the point that epsilon can only be larger than \alpha_n if n becomes extremely small? Sincerely Yours BeoWulf

Convergens of Cesáros mean(Urgent). Homework Statement I need to show the following: (1) Let number sequence be given called \{\alpha_{n}\}_{n=1}^{\infty} for which \alpha_{n} \rightarrow 0 where n \rightarrow \infty. (2) Given a sequence \{\beta_{n}}\}_{n=1}^{\infty} which is...

Hello Hallsoft: Thank You for Your reply. I am sorry that the context of the problem was not clear. Here is the problem in its full context: Suppose we throw a red and white die simultaneously. The possible outcome of an experiment such as this can be recorded as follows: S =...

Question(a) This will only work if P(TU) = 0? By this you mean proving that P(TU) = emptyset. The only that I know here is the that is the consequence of the formula P(T U U) = P(T) + P(U). Is that what you mean?? Question(b) Since nothing is said about the events being...

Homework Statement Given S = \{(r,w)| r,w = 1,2,\ldots, 6\} Deduce the following three probability functions. Probability that the number of eyes are red (1)P_{R}(t) = \frac{1}{6} for t \in \{1,2,\ldots 6 \} Probability that the number of eyes are either red or white...

Homework Statement An honest coin is throughn again and again until two consigutive heads or tails appears. Assume that the troughs are independent. Let T be the number of throughs which can take on the values 2,3,... Calculate P(T = n) for n = 2,3,... The Attempt at a Solution...

Hello Again, The whole problem is as follows: Let (S, E, P) be a probability space and let T and U be events(Nothing is said about the events). Show, that if (1) P(T) = P(U) = 0 then P(T \cup U) = 0 (2) P(T) = P(U) = 1 then P(T \cap U) = 1 My Solultion(1):P(T \cup U) = P(T) +...

From what I see it P(T \cap U) cannot be larger than one for obvious reasons. Because that would give a negative probability. I am not sure about that, another way of proving question (2) Could it say If P(C) is the entire probability space where then since P(T) = P(U), then I could say...

Homework Statement Given that P(T) = P(U) = 0 then show that P(T \cup U) = 0 Given that P(T) = P(U) = 1 then show that P(T \cap U) = 1 Homework Equations I am told that I need to use the following equations. (1) P(T \cup U) = P(T) + P(U) if P(T \cap U) = 0 (2) P(T \cup U) =...