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  1. D

    Notes on Probability

    Proof. By definition, equally likely events have equal probability of happening. Suppose that the probabilty is p. Since we are sure that something will happen, the total probability of the events is equal to 1. Hence we have Obviously p=1/n. Hence the probability of each event is equal to...
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    Limit problem

    I thank for your replies. I was definitely making it much harder than it should have been.
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    Limit problem

    I know that I need only to find a sing delta given an epsilon, but without knowing a, what good is knowing that |x - a| < 1?, for instance. What about considering the open interval (-∞, 0) U (0, ∞)? With this, I can show that for any x in I, the limit goes to zero, correct? Could you elaborate...
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    Limit problem

    |f(x) - L| = |f(x) - 0| = |f(x)| < ϵ. Given the definition of the function, the only way this holds is if x is nonzero. At this point I tried to consider 0 < |x - a| < δ. I'm trying to show that you can pick a δ such that i dunno...
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    Limit problem

    If f(x) = 0 for all nonzero x and f(0) = some constant c, how can you show that lim = 0 for any x as x approaches a? I tried using the definition of limit, but this is going nowhere.
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    Setting up Kolmogorov's Backward Equations

    So you use a matrix to solve the transition probabilities in the backwards equations? Can you elaborate on this. I am using Ross's book "Introduction to Probability Models" and he doesn't explain how to do this, at least not in this section.
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    Setting up Kolmogorov's Backward Equations

    Consider two machines, both of which have an exponential lifetime with mean 1/λ. There is one repairman who can service machines at an exponential rate of μ. How does one set up the Kolmogorov backward equations for such a scenario? I am not sure after finding the rates how to work those...
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    Bijections between sequences.

    Thanks for the replies. I realized that the bijection doesn't tell you anything using a counterexample similar to that one right after I posted :(
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    Bijections between sequences.

    Consider two sequences, {a_n} and {b_n}. If there is a one-to-one correspondence between these sets, can we conclude anything about their behavior considering, say, that we know that one is convergent? Going further, can we conclude anything about the series resulting from these sequences?
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    Convergent Subsequences

    Yes, although I still feel uncomfortable putting something down without knowing how to write a formula for it. I know that it isn't necessary, but it just seems a little more solid to me.
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    Convergent Subsequences

    I believe that I see what you are hinting at: Is this legal, and if so, is it correct? {1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, ... }
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    Convergent Subsequences

    This sequence with subsequences converging to every natural number is definitely not as analogous as I thought it would be to the previous problem. I'll keep thinking about it, but if anyone has some helpful suggestions or hints then I would be glad to read them. Thank you for all the help thus far.
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    Convergent Subsequences

    Would this work? {.9, .99, .999, ...... , 1.9, 1.99, 1.999, ..... 2.9, 2.99, 2.999, .....}
  14. D

    Convergent Subsequences

    Yes, it is exceedingly obvious by looking at the first portion of the sequence written out, but I am just trying to be rigorous. Thank you.
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    Convergent Subsequences

    Sorry to nag, but you are saying that that is enough of an answer? What would the formula for that sequence be?
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    Convergent Subsequences

    Do you not need an explicit formula? Does that even converge to anything but 0?
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    Convergent Subsequences

    What is the explicit formula for that? I am getting too tired thinking about this for so long. I can see having two limits, but three?
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    Convergent Subsequences

    I am having a hard time finding a starting point for these problems. One is to find a sequence with subsequences that converge to 1, 2, and 3. A similar problem (which would solve both problems) is to find a sequence that has subsequences that converge to every positive integer. I am not...
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    Friends,i thought i'd share this poem i wrote to my wonderful

    It is so refreshing to see an amateur poet (in terms even of the very essence of the word) to write something like this. Poetry is art, not an upchucking of emotion... or something like that. I think the poem would be even better if you could rewrite part of the second stanza. Maybe consider...
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    How do we calculate the E(max(x,y))

    First, using order statistics, find the probability of the maximum of x and y. That is, Y(n) = n * f(y) * [F(y)]^(n-1) Use the probability density function for f(y), and the cumulative distribution function for F(y) (or just integrate the density function f(y)). Once you have Y(n), finding...
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    Calculators Should i bother getting a graphing calculator?

    I agree with this. It is one thing if the curriculum demands that each student use a graphing calculator, but as someone who has been through math in college, I think that the presence of graphing calculators in high school and even below are very damaging. Analytical methods are very...
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    Linear maps and composites HELP!

    I think they may be asking you to show that Ui is invertible (non-singular), with some given parameters. Try to relate the statements about the rank of the matrix to properties that imply non-singularity.
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    C/++/# What is so special about running a c++ program through commnd line?

    That part is obvious. I was trying to look for input from people who have strong and founded opinions about using command line.
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    C/++/# What is so special about running a c++ program through commnd line?

    I.e., what is beneficial about main(int argc,char *argv[])? I see a lot of seemingly good programmers write the main like this, but what does it do that int main() cannot do?
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    Windows 7 USB Error

    I will try my web cam and see if that works. I am just confused why my device will power up and then windows will give me an error. I have tried all slots with the same result. I just can't help but think that it is software related.
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    Windows 7 USB Error

    I have not tried the G5 on any other computers but I did use two other mice from working computers to try to trouble shoot with and windows could still not recognize the usb device. I used my old wireless mouse and keyboard from logitech, which is one part usb and the other part is the older...
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    Windows 7 USB Error

    I recently built a new computer off newegg. Put everything together without a hitch, and order Windows 7 oem. I proceeded to install windows 7. Once the download was complete, I went to use my mouse, it didn't work. I figured this as being no big deal seeing as how I did not install my...
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    GMAT math question

    f(x) is just the function f evaluated at x. This question wants to know which of the listed functions is such that f(x) gives the same output as f(x - 1).
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    Statistics Need Help 1

    Is this in regards to what I wrote? I am very much a neophyte of statistics, especially compared to you, but how does the number of students and the idea of a percentage achieving an average located above a certain number change the problem? Is Chebysheff's Inequality a viable means to a solution?
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    Statistics Need Help 1

    Try setting up a solution using Chebycheff's Inequality: P(|Y - µ| >= kσ) <= 1/k^2 We know that µ is the mean, which equals 2.725, and that σ is the square root of variance (i.e., the standard deviation, which is 1.329).
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