# determining if it is convergent or divergent + taylor series

Hello Jt, since this is a wiki you don't need to address your questions to me. Anyone is free to answer them.

Let's see:

1. The integral from a to b over the function needs to equal 1. Hence A = 1/integral. See, e.g. here.

2. I'm not sure if I get where your confusion comes from. But a coin toss is *the* classical example of a Bernoulli distribution. Here *p* = 0.5, hence *q* = 1-*p* = 0.5. If you let *Head* be a *success*, then the probability of 3 successes is as asserted.

3. I'm not sure which question you are referring to. But if the question is something like *it is twice as likely that roll a 6 than any other number* you do the following: Let *a* be the probability of *any other number*. Then 2*a* is the probability of a 6. The total probability needs to be 1. With this information you can find *a*: *a*+*a*+*a*+*a*+*a*+2*a* = 1, i.e. *a* = 1/7 and thus prob(6) = 2/7.

4. The normalized binomial is needed to justify the use of a continuous random variable (with Gaussian as pdf) as an approximation to a discrete random variable (with binomial pdf). So in this sense it motivates chapter 8. In *real life* this is extremely useful in [Statistical hypothesis testing, but we didn't go into details here so I don't think you should worry about it.

5. Of course I can't comment on your first question. But yes, this is an example that, mathematically, it is the same as tossing a coin. But the application can we very different and easily applicable to a real world problem. Same with Hardy Weinberg genetics, since this relies on the binomial distribution (and is hence mathematically the same as a coin toss) you can apply the theoretical results on the binomial to genetics.

Hope this helps. Your questions are very welcome :)

thanks so much for the clarification! :D