Recent content by tomwilliam

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    Calculate the area of this pond with functions given for the perimeter

    So the solution is obviously given here, I'm just trying to understand it. I thought that integrating f(x) from -5 to 5 would give the area under the curve (including the areas below the "pond" at the edges of the image but above y=0. I don't really understand why we are subtracting the integral...
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    NHST statistics for % of students late to class

    Doesn’t that make me correct? The ##H_a: p > 0.2## corresponds to the teachers’ assertion being supported by the data, right ? Whereas H_0 would be that the teachers’ claim is not supported? (Although I’m not sure why it isn’t ##H_0: p < 0.2## What am I missing? Thanks!
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    NHST statistics for % of students late to class

    Thanks for all of your help. Indeed, this is two separate questions. Sorry if that wasn’t clear. I do have a follow up about the equalities/inequalities. We had worked on the basis of p > or equal to 0.2, given that it says « at least 20% ». Why is it = for the null hypothesis and inequality for...
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    NHST statistics for % of students late to class

    This is a homework question in my daughter’s maths class. When I did stats I always had examples where there were two variables : an example being swallow wingspan and sex. The statement that males have larger wingspan would therefore be the H_1 and the H_0 would be that there is no impact of...
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    Chance of Selecting Twins from Group of 30 [Solved!]

    Thank you! So I’m brute force calculating it and I see 6 possible ways, each of which have 28 different arrangements. This would be 168 in the numerator, out of 4060 possible outcomes = 0.04. I’m not sure what formula to use to avoid the brute force counting: would it be Permutations? I thought...
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    Chance of Selecting Twins from Group of 30 [Solved!]

    Thanks to all for your help. So now I'm looking at all of the possible permutations of Twin 1...Twin 2....Any of the other 28. I figure that it could be 6 different permutations x 28 for each of the others. That would give me 162 permutations which are favourable, divided by 4060 possible...
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    Chance of Selecting Twins from Group of 30 [Solved!]

    Yes, that's what makes me think I've got it wrong. I think what I have is the same as the probability of selecting the two twins when choosing two out of the thirty. I have an extra available slot, but how do I factor that into the probability?
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    Chance of Selecting Twins from Group of 30 [Solved!]

    TL;DR Summary: Chance of picking 2 named people when randomly choosing 3 from a group of 30. For my daughter's homework question: There is a group of 12 girls and 18 boys. Two of them are twins (girl and boy). If I select three at random, what is the chance that the twins will be chosen? I...
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    Probability of Receiving 2-4-6-7-Queen-King Sequence from 40 Cards

    Thank you! I considered this possibility, but discarded it on the following logic: If the question means that the sequence has to be all of the same suit, it should still be a factor of 4 in answer (C), as there are four possible suits for it to work with. If the question wants a specific...
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    Probability of Receiving 2-4-6-7-Queen-King Sequence from 40 Cards

    A quick translation of the question: We have a deck of 40 cards, containing four suits (hearts, diamonds, spades, clubs), in which each suit has an ace, a queen, a jack, a king and six number cards (2 to 7). From the deck, six cards are distributed randomly and successively to a player who picks...
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    I How to Differentiate Using the Chain Rule?

    Thanks to both of you...I understand it now.
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    I How to Differentiate Using the Chain Rule?

    Ok, thanks, I see where my mistake came in. So now I have ## \frac{d\sqrt{u}}{du}=(1/2)u^{-1/2} ## and ## \frac{du}{d\epsilon}= 2(y' + \epsilon g') ## so ## \frac {df}{d\epsilon} = (1/2)u^{-1/2}\times 2(y' + \epsilon g') ## but I seem to be a factor of ##g'## out.
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    I How to Differentiate Using the Chain Rule?

    I'm coming back to maths (calculus of variations) after a long hiatus, and am a little rusty. I can't remember how to do the following derivative: ## \frac{d}{d\epsilon}\left(\sqrt{1 + (y' + \epsilon g')^2}\right) ## where ##y, g## are functions of ##x## I know I should substitute say ##u = 1...
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