# 14.5 Formulas

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This module provides an overview of Statistics Formulas used as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.
Formula

## Factorial

$n!=n\left(n-1\right)\left(n-2\right)...\left(1\right)\text{}$

$0!=1\text{}$

Formula

## Combinations

$\left(\genfrac{}{}{0}{}{n}{r}\right)=\frac{n!}{\left(n-r\right)!r!}\text{}$

Formula

## Binomial distribution

$X~B\left(n,p\right)$

$P\left(X=x\right)=\left(\genfrac{}{}{0}{}{n}{x}\right){p}^{x}{q}^{n-x}$ , for $x=0,1,2,...,n$

Formula

## Geometric distribution

$X~G\left(p\right)$

$P\left(X=x\right)={q}^{x-1}p$ , for $x=1,2,3,...$

Formula

## Hypergeometric distribution

$X~H\left(r,b,n\right)$

$P\left(X=x\right)=\left(\frac{\left(\genfrac{}{}{0}{}{r}{x}\right)\left(\genfrac{}{}{0}{}{b}{n-x}\right)}{\left(\genfrac{}{}{0}{}{r+b}{n}\right)}\right)$

Formula

## Poisson distribution

$X~P\left(\mu \right)$

$P\left(X=x\right)=\frac{{\mu }^{x}{e}^{-\mu }}{x!}$

Formula

## Uniform distribution

$X~U\left(a,b\right)$

$f\left(X\right)=\frac{1}{b-a}$ , $a

Formula

## Exponential distribution

$X~\mathrm{Exp}\left(m\right)$

$f\left(x\right)=m{e}^{-\mathrm{mx}}$ , $m>0,x\ge 0$

Formula

## Normal distribution

$X~N\left(\mu ,{\sigma }^{2}\right)$

$f\left(x\right)=\frac{1}{\sigma \sqrt{2\pi }}{e}^{\frac{{-\left(x-\mu \right)}^{2}}{{2\sigma }^{2}}}$ , $\phantom{\rule{12pt}{0ex}}-\infty

Formula

## Gamma function

$\Gamma \left(z\right)={\int }_{0}^{\infty }{x}^{z-1}{e}^{-x}\mathrm{dx}$ $z>0$

$\Gamma \left(\frac{1}{2}\right)=\sqrt{\pi }$

$\Gamma \left(m+1\right)=m!$ for $m$ , a nonnegative integer

otherwise: $\Gamma \left(a+1\right)=\mathrm{a\Gamma }\left(a\right)$

Formula

## Student-t distribution

$X~{t}_{\mathrm{df}}$

$f\left(x\right)=\frac{{\left(1+\frac{{x}^{2}}{n}\right)}^{\frac{-\left(n+1\right)}{2}}\Gamma \left(\frac{n+1}{2}\right)}{\sqrt{\mathrm{n\pi }}\Gamma \left(\frac{n}{2}\right)}$

$X=\frac{Z}{\sqrt{\frac{Y}{n}}}$

$Z~N\left(0,1\right)$ , $Y~{Χ}_{\mathrm{df}}^{2}$ , $n$ = degrees of freedom

Formula

## Chi-square distribution

$X~{Χ}_{\mathrm{df}}^{2}$

$f\left(x\right)=\frac{{x}^{\frac{n-2}{2}}{e}^{\frac{-x}{2}}}{{2}^{\frac{n}{2}}\Gamma \left(\frac{n}{2}\right)}$ , $x>0$ , $n$ = positive integer and degrees of freedom

Formula

## F distribution

$X~{F}_{\mathrm{df}\left(n\right),\mathrm{df}\left(d\right)}$

$\mathrm{df}\left(n\right)=$ degrees of freedom for the numerator

$\mathrm{df}\left(d\right)=$ degrees of freedom for the denominator

$f\left(x\right)=\frac{\Gamma \left(\frac{u+v}{2}\right)}{\Gamma \left(\frac{u}{2}\right)\Gamma \left(\frac{v}{2}\right)}{\left(\frac{u}{v}\right)}^{\frac{u}{2}}{x}^{\left(\frac{u}{2}-1\right)}\left[1+\left(\frac{u}{v}\right){x}^{-.5\left(u+v\right)}\right]$

$X=\frac{{Y}_{u}}{{W}_{v}}$ , $Y$ , $W$ are chi-square

Apply social psychology on real life in Nigerian universities campus
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I am here for the first time just here to learn...
hi I'm new on here first time
Lisa
hello
GOPAL
hi,am new here
jennifer
what is this group all about
jennifer
Suppose an individual with OCD experiences obsessive thoughts about germs, contamination, and disease whenever she encounters a doorknob. What might have constituted a viable unconditioned stimulus?
What are factors that influence learning?
Environment Heredity(I am not sure about heredity)
Tusita
Enos
Sure, anytime
Tusita
I have other questions also
Enos
Based on the factors affecting learning, how do we improve learning
Enos
I think that addressing that everyone learns in their own time
James
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Sorie
Also knowing what's going on at home. what pressure are the parents putting on them.
James
am I close or no
James
also is there a lack of care? going one more step. with peer groups do an activity that shows how much they have in common
James
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getting passionate about something and strive for success
Leanne
observation and method based
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Winter
soul is the Greek word for psyche
Winter
psychology is scientific research of the human brain.
Winter
Psychology is a study of human mind and behaviour
Vaishnavi
psychology is a social science which aim at studying the mind as it affect the behavior of an individual.
Prince
write and explain four psychosexual stages of personality development
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yes
Beverly
whats the age of the boy?
Beverly
16 or 17
Ajayi
lol. it gets over with time. it's not something that can be changed instantly. and for teenagers.. anyone of opposite sex is a tasty lollipop.
Alex
yes in time it will go away but could also take years
Beverly
maybe because he doesn't really have mind of making decisions at the moment on what he need and what he doesn't want
Nwokwu
maybe he's trying to find someone to love because he's either lacked loved and feel that's the only way to feel loved or he's lonely and feels a girl can make it better . either he's got deal with the core issue
Jonan
its natural. I think it should be like this. girls also have weakness toward guys. but you can overcome on few things like concept of beauty. first step is realisation which will grow in you. also discipline help in these things.
Sujeet
what are cluster A disease?
because psychology is a natural science as well as a science. it's a interdisciplinary subject
yes absolutely we cabt out Psychology completely into science dur to its various measuring aspects
utkarsh
cannot* put*
utkarsh
1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.