Self review: Statistics - Binomial Distribution

[eehiram]

Homework Statement

The Binomial Distribution - already developed by Jacob Bernoulli (in 1713), et alii, before Abraham de Moivre (1667-1754 CE), et alii, developed the Normal Distribution as an approximation for it (id est, the Binomial Distribution) - gives the discrete probability distribution P_p (n|N) of obtaining exactly n successes out of N Bernoulli trials (where the result of each Bernoulli trial is true with probability p and false with probability q=1-p). Next: Normal Distribution...

Homework Equations

$$P_p (N|n) = \binom{N}{n}p^n q^{N-n}$$

The Attempt at a Solution

$$P_p (N|n) = \frac{N!}{n! (N-n)!} p^n (1-p)^{N-n}$$

This has been an attempt at self-review; and a chance to learn to use LaTex. Thanks for any replies to check my work!

 

[eehiram]

History of Binomial Coefficient

I have found a PDF online of the history of the Binomial Coefficient, tracing the many sources, exempli gratia:

a) Michael Stifel, Arithmetica Integra, 1544 CE

b) Blaise Pascal (1623-1662 CE), and his famous Pascal's Triangle

c) James Gregory, 1670 CE

d) Sir Isaac Newton, letter, October 1676 CE

I can post the link if requested to do so; such information is easy to find online and in textbooks and history-of-mathematics books.

 

[LCKurtz]

Homework Statement

The Binomial Distribution - already developed by Jacob Bernoulli (in 1713), et alii, before Abraham de Moivre (1667-1754 CE), et alii, developed the Normal Distribution as an approximation for it (id est, the Binomial Distribution) - gives the discrete probability distribution P_p (n|N) of obtaining exactly n successes out of N Bernoulli trials (where the result of each Bernoulli trial is true with probability p and false with probability q=1-p). Next: Normal Distribution...

Homework Equations

$$P_p (N|n) = \binom{N}{n}p^n q^{N-n}$$

The Attempt at a Solution

$$P_p (N|n) = \frac{N!}{n! (N-n)!} p^n (1-p)^{N-n}$$

This has been an attempt at self-review; and a chance to learn to use LaTex. Thanks for any replies to check my work!

What is there to check? That you wrote the binomial coefficient correctly? If that's your question, yes you did. Otherwise, what is your question?

 

[eehiram]

Thanks for the feedback; I'm not sure, yet...

I appreciate the feedback. Thank you for verifying my correct posting with LaTex of the equations. (These were my 1st uses of LaTex.)

The derivations are not included; I tried to post in 2.5 hours, as it was my first time using the homework help sub-forum. So, I had to skip any additional content.

Thank you for your patience with me. There are several mathematical stages to Normal Distribution; this was intended to be one of them.

If encouraged to do so, I would like to post a few more equations pertaining to Normal Distribution and the buildup to such.

I'm trying to review the material from my probability and statistics textbook from 20 years ago; I haven't come up with an explicit question to ask about yet... Any interest in buildup to Normal Distribution is still appreciated!

 

[eehiram]

Question on deviations from Normal Distribution

I have come up with a few questions, and will need to start a new thread for:
Normal Distribution:

1. What are the easiest analyses of deviations from Normal Distribution? (Exempli gratia: mean, variance, skewness, kurtosis)?

2. What is the frequency of departures from Normal Distribution when considering near-to-Normal Distribution data? (BTW the data need not be real data.)

3. How is the Gaussian Function resolved, as the probability density function of the Normal Distribution?

Thank you for replying. I intend to start the Normal Distribution thread soon, with the equation for Normal Distribution in LaTex again, and post my questions there as well.

 

[eehiram]

Normal Distribution - self study / review

Please see my new thread, "Normal Distribution - self study / review":

for a thread on Normal Distribution, beginner's deviations from such, and a few other questions.
Thanks!