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comment Probability that a quadratic polynomial with random coefficients has real roots
Thanks for answering. I upvoted your answer, but didn't select it as answer because I ended up doing it Shai Covo's way. Yours would probably be easier if my calculus wasn't so rusty, though.
Mar
27
comment Probability that a quadratic polynomial with random coefficients has real roots
Thanks a lot. I'll still need to think about it, but now I'm sure you've given me all the basis I needed.
Mar
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accepted Probability that a quadratic polynomial with random coefficients has real roots
Mar
27
comment Probability that a quadratic polynomial with random coefficients has real roots
Taking log on both sides, I want $P(-2(-\log B)\geq\log 4-\left[-\log A+\left(-\log C\right)\right])$, right? With $-\log B$ exponential(1) and $\left[-\log A+\left(-\log C\right)\right]$ a gamma distribution. I'm still having trouble getting to the integral you wrote. I'm just starting to study about pdfs, so a lot is new to me. Where does $\log 4$ goes? How do I compare two random variables to see the prob. that one is greater? I was hoping you could walk this newbie a bit further along the path -- or provide me with some reference on manipulating random variables. Thanks!
Mar
27
comment Probability that a quadratic polynomial with random coefficients has real roots
Thanks for answering. I'm having a bit of trouble calculating all those distributions. Do you have any references that could help me out? Preferably online, but a good book will do as well. I'm just starting to learn about probability distributions, so I'm still not sure how to manipulate random variables algebraically. Again, thank you.
Mar
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asked Probability that a quadratic polynomial with random coefficients has real roots
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accepted Choosing probabilities as to make a coin game fair
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revised Choosing probabilities as to make a coin game fair
formatting
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comment Choosing probabilities as to make a coin game fair
This is really clever. Is this kind of recursive thinking common in a lot of probability problems?
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asked Choosing probabilities as to make a coin game fair