Recent content by Agent Smith

I shall have to revisit the concept. @Dale and @FactChecker . Thanks

@FactChecker & @Dale 👇 I want to test if a coin is biased/not. H = The coin is biased D = The data/evidence (70 heads in 100 flips) P(H) = 0.5 (prior probability) ##P(H|D) = \frac{P(H) \times P(D|H)}{P(D)}## For a head-biased coin, P(heads) = 0.7 mean = 0.7 standard deviation = ##\sigma_H =...

Thank you. I do understand a bit of the ROPE (region of practical equivalence) trick :smile: you mentioned. For this particular case (biased coin hypothesis), the ROPE is a range e.g. [0.45, 0.55] for the proportion of heads you would consider to be an outcome for a fair coin. It seems there's a...

In discussions with other people, some of them were kind enough to acknowledge that my method and results, as they appear in the OP, can be considered a crude, informal, imprecise way to check for a biased coin. @Dale was right to point out that I should've computed ##P(X \geq 70)## for the...

My question is whether a biased coin can have P(heads) = P(tails) = 0.5. Thank you for the answer though. It went over my head, but I have saved your comments in my notes, for later study.

@Dale a question on Bayes' theorem. If my prior probability that the coin is biased = 0.7, can the probability of heads = 0.5? I need the probability of heads to compute P(k heads | coin is biased) = P(evidence|hypothesis). Also I feel that P(coin is biased) = P(heads for a head-biased coin) =...

I formed my hypotheses before the results of my experiment. I conducted the experiment to test my hypotheses. I suppose you're correct. I was worried about that. The probability of HHHHT (for example) = probability of HTTTT. Not sure about that since the former is ##^{100}C_{70} \times 0.5^{70}...

I have a coin. I flip it a 100 times and see that 70 of the outcomes are heads. ##H_0##: Assume coin is fair i.e. P(heads) = P(tails) = 0.5 ##H_a##: The coin is biased (towards heads) ##\alpha = 0.05## Under ##H_0##, ##\text{p value } = P(70 \text{ heads}) = ^{100}C_{70} \times 0.5^{70} \times...

What is this

We can still test the probability of the hypothesis, but it looks as though posterior probability < prior probability because(?) ##P(\neg D|H)## is going to be low.

💯

Not everyday is Sunday I suppose. 🏖️ It's said that in today's world there can be no polymaths.

@Dale and @FactChecker I think the discussion we've had is adequate for my level. Thank you. One last question. For Bayes' theorem given as ##P(H|D) = \frac{P(H) \times P(D|H)}{P(D)}##, the Wikipage says that ##P(D) \ne 0## (division by ##0##). But I noticed that since ##P(\neg A) = 1 -...

This is the binomial theorem I believe. So this is the probability of the evidence given the hypothesis. So I've flipped the coin ##1000## times and I get ##490## heads, that's a heads proportion = ##0.49##. You said ##H = 0.5##. I don't quite get that. Shouldn't it be ##H = 0.49##. Is the...

@Dale Too advanced a topic for me, but I have a much better grasp of what's going on. Here's where I trip up: 1. I don't know what's a ##\beta## distribution (you linked me to the Wikipage. :thumbup: ) 2. I didn't quite get this 👇 My brain's telling me ##E## and ##H## aren't numbers and so I...