Recent content by tomwilliam

Just chatting with my son about Maths and he casually mentioned that 0 would be the midpoint of the number line from -inf to +inf. I wondered whether it wouldn’t be more accurate to say there is no single midpoint. Couldn’t you make an argument that any real number is exactly halfway between...

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...

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!

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...

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...

Thanks to everyone for helping!

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...

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...

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?

Ah! Is it P=2/30 x 1/29 x 28/28?

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...

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...

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...

Thanks to both of you...I understand it now.

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.