• https://math.stackexchange.com/questions/2033370/how-to-determine-the-number-of-coin-tosses-to-identify-one-biased-coin-from-anot/2033739#2033739 Suppose there are two coins and the percentage that each coin flips a Head is $$p$$ and $$q$$, respectively. $$p, q \in [0,1]$$ and the values are given and known. If you are free to flip one of the coins, how many times $$n$$ do you have to flip the coin to decide with some significance level $$\left( \textrm{say } \alpha = 0.05 \right)$$ that it’s the $$p$$ coin or the $$q$$ coin that you’ve been flipping? The distribution of heads after $$n$$ flips for a coin will be a binomial distribution with means at $$pn$$ and $$qn$$. The Usual Hypothesis Test In the usual hypothesis…

• Test The Usual Colors of the Sky Why is the sky blue? Why are sunsets red? The answers and explanations to these questions can be found fairly easily on the internet. But there are many subtle “Wait a minute…”-type questions in between the cracks that seem to necessitate subtle answers and more “difficult” searching around the internet to find those answers. So, why is the sky blue? No, but first, what color is sunlight? Visible light generally is from 390 nm (violet) to 720 nm (red). Visible sunlight is a mix of these colors at the intensities we see in the figure above. , with maximum eye sensitivity at 555…