{"id":2299,"date":"2017-06-15T22:03:05","date_gmt":"2017-06-15T22:03:05","guid":{"rendered":"http:\/\/10.10.10.4:9191\/softlect\/?p=2299"},"modified":"2019-06-20T14:56:05","modified_gmt":"2019-06-20T14:56:05","slug":"probability-symbols","status":"publish","type":"post","link":"http:\/\/softlect.com\/index.php\/probability-symbols\/","title":{"rendered":"Probability Symbols"},"content":{"rendered":"

Probability Symbols table<\/h2>\n

 <\/p>\n

\n
\n
Symbol<\/strong><\/div>\n
Symbol Name<\/strong><\/div>\n
Meaning \/ definition<\/strong><\/div>\n
Example<\/strong><\/div>\n<\/div>\n
\n
P<\/em>(A<\/em>)<\/div>\n
probability function<\/div>\n
probability of event A<\/div>\n
P<\/em>(A<\/em>) = 0.5<\/div>\n<\/div>\n
\n
P<\/em>(A<\/em> \u2229 B<\/em>)<\/div>\n
probability of events intersection<\/div>\n
probability that of events A and B<\/div>\n
P<\/em>(A<\/em>\u2229B<\/em>) = 0.5<\/div>\n<\/div>\n
\n
P<\/em>(A<\/em> \u222a B<\/em>)<\/div>\n
probability of events union<\/div>\n
probability that of events A or B<\/div>\n
P<\/em>(A<\/em>\u222aB<\/em>) = 0.5<\/div>\n<\/div>\n
\n
P<\/em>(A<\/em> | B<\/em>)<\/div>\n
conditional probability function<\/div>\n
probability of event A given event B occured<\/div>\n
P<\/em>(A | B<\/em>) = 0.3<\/div>\n<\/div>\n
\n
f <\/em>(x<\/em>)<\/div>\n
probability density function (pdf)<\/div>\n
P<\/em>(a <\/em>\u2264 x <\/em>\u2264 b<\/em>) = \u222b f <\/em>(x<\/em>)dx<\/em><\/div>\n
<\/div>\n<\/div>\n
\n
F<\/em>(x<\/em>)<\/div>\n
cumulative distribution function (cdf)<\/div>\n
F<\/em>(x<\/em>) = P<\/em>(X <\/em>\u2264 x<\/em>)<\/div>\n
<\/div>\n<\/div>\n
\n
\u03bc<\/em><\/div>\n
population mean<\/div>\n
mean of population values<\/div>\n
\u03bc<\/em> = 10<\/div>\n<\/div>\n
\n
E<\/em>(X<\/em>)<\/div>\n
expectation value<\/div>\n
expected value of random variable X<\/div>\n
E<\/em>(X<\/em>) = 10<\/div>\n<\/div>\n
\n
E<\/em>(X | Y<\/em>)<\/div>\n
conditional expectation<\/div>\n
expected value of random variable X given Y<\/div>\n
E<\/em>(X | Y=2<\/em>) = 5<\/div>\n<\/div>\n
\n
var<\/em>(X<\/em>)<\/div>\n
variance<\/div>\n
variance of random variable X<\/div>\n
var<\/em>(X<\/em>) = 4<\/div>\n<\/div>\n
\n
\u03c32<\/sup><\/em><\/div>\n
variance<\/div>\n
variance of population values<\/div>\n
\u03c32 <\/sup><\/em>= 4<\/div>\n<\/div>\n
\n
std<\/em>(X<\/em>)<\/div>\n
standard deviation<\/div>\n
standard deviation of random variable X<\/div>\n
std<\/em>(X<\/em>) = 2<\/div>\n<\/div>\n
\n
\u03c3X<\/sub><\/em><\/div>\n
standard deviation<\/div>\n
standard deviation value of random variable X<\/div>\n
\u03c3X<\/sub><\/em>=2<\/div>\n<\/div>\n
\n
\"\"<\/div>\n
median<\/div>\n
middle value of random variable x<\/div>\n
\"\"<\/div>\n<\/div>\n
\n
cov<\/em>(X<\/em>,Y<\/em>)<\/div>\n
covariance<\/div>\n
covariance of random variables X and Y<\/div>\n
cov<\/em>(X,Y<\/em>) = 4<\/div>\n<\/div>\n
\n
corr<\/em>(X<\/em>,Y<\/em>)<\/div>\n
correlation<\/div>\n
correlation of random variables X and Y<\/div>\n
corr<\/em>(X,Y<\/em>) = 0.6<\/div>\n<\/div>\n
\n
\u03c1<\/em>X<\/em>,Y<\/em><\/sub><\/div>\n
correlation<\/div>\n
correlation of random variables X and Y<\/div>\n
\u03c1<\/em>X<\/em>,Y<\/em><\/sub> = 0.6<\/div>\n<\/div>\n
\n
\u2211<\/div>\n
summation<\/div>\n
summation – sum of all values in range of series<\/div>\n
\"\"<\/div>\n<\/div>\n
\n
\u2211\u2211<\/div>\n
double summation<\/div>\n
double summation<\/div>\n
\"\"<\/div>\n<\/div>\n
\n
Mo<\/em><\/div>\n
mode<\/div>\n
value that occurs most frequently in population<\/div>\n
<\/div>\n<\/div>\n
\n
MR<\/em><\/div>\n
mid-range<\/div>\n
MR<\/em> = (xmax<\/sub><\/em>+xmin<\/sub><\/em>)\/2<\/div>\n
<\/div>\n<\/div>\n
\n
Md<\/em><\/div>\n
sample median<\/div>\n
half the population is below this value<\/div>\n
<\/div>\n<\/div>\n
\n
Q1<\/sub><\/div>\n
lower \/ first quartile<\/div>\n
25% of population are below this value<\/div>\n
<\/div>\n<\/div>\n
\n
Q2<\/sub><\/div>\n
median \/ second quartile<\/div>\n
50% of population are below this value = median of samples<\/div>\n
<\/div>\n<\/div>\n
\n
Q3<\/sub><\/div>\n
upper \/ third quartile<\/div>\n
75% of population are below this value<\/div>\n
<\/div>\n<\/div>\n
\n
x<\/em><\/div>\n
sample mean<\/div>\n
average \/ arithmetic mean<\/div>\n
x <\/em>= (2+5+9) \/ 3 = 5.333<\/div>\n<\/div>\n
\n
s<\/em>2<\/sup><\/div>\n
sample variance<\/div>\n
population samples variance estimator<\/div>\n
s<\/em>2<\/sup> = 4<\/div>\n<\/div>\n
\n
s<\/em><\/div>\n
sample standard deviation<\/div>\n
population samples standard deviation estimator<\/div>\n
s<\/em> = 2<\/div>\n<\/div>\n
\n
zx<\/sub><\/em><\/div>\n
standard score<\/div>\n
zx<\/sub><\/em> = (x<\/em>-x) \/ sx<\/sub><\/em><\/div>\n
<\/div>\n<\/div>\n
\n
X <\/em>~<\/div>\n
distribution of X<\/div>\n
distribution of random variable X<\/div>\n
X <\/em>~ N<\/em>(0,3)<\/div>\n<\/div>\n
\n
N<\/em>(\u03bc<\/em>,\u03c3<\/em>2<\/sup>)<\/div>\n
normal distribution<\/div>\n
gaussian distribution<\/div>\n
X <\/em>~ N<\/em>(0,3)<\/div>\n<\/div>\n
\n
U<\/em>(a<\/em>,b<\/em>)<\/div>\n
uniform distribution<\/div>\n
equal probability in range a,b<\/div>\n
X <\/em>~ U<\/em>(0,3)<\/div>\n<\/div>\n
\n
exp<\/em>(\u03bb)<\/div>\n
exponential distribution<\/div>\n
f <\/em>(x<\/em>) = \u03bbe<\/em>–\u03bbx<\/em><\/sup> , x<\/em>\u22650<\/div>\n
<\/div>\n<\/div>\n
\n
gamma<\/em>(c<\/em>, \u03bb)<\/div>\n
gamma distribution<\/div>\n
f <\/em>(x<\/em>) = \u03bb c x<\/em>c-1<\/sup>e<\/em>–\u03bbx<\/em><\/sup> \/ \u0393(c<\/em>), x<\/em>\u22650<\/div>\n
<\/div>\n<\/div>\n
\n
\u03c7 2<\/sup>(k<\/em>)<\/div>\n
chi-square distribution<\/div>\n
f <\/em>(x<\/em>) = xk<\/sup><\/em>\/2-1<\/sup>e<\/em>–x<\/em>\/2<\/sup> \/ ( 2k\/2 <\/sup>\u0393(k<\/em>\/2) )<\/div>\n
<\/div>\n<\/div>\n
\n
F <\/em>(k<\/em>1<\/sub>, k<\/em>2<\/sub>)<\/div>\n
F distribution<\/div>\n
<\/div>\n
<\/div>\n<\/div>\n
\n
Bin<\/em>(n<\/em>,p<\/em>)<\/div>\n
binomial distribution<\/div>\n
f <\/em>(k<\/em>) = n<\/sub>Ck<\/sub> pk<\/sup><\/em>(1-p<\/em>)n-k<\/sup><\/em><\/div>\n
<\/div>\n<\/div>\n
\n
Poisson<\/em>(\u03bb)<\/div>\n
Poisson distribution<\/div>\n
f <\/em>(k<\/em>) = \u03bbk<\/sup>e<\/em>–\u03bb<\/em><\/sup> \/ k<\/em>!<\/div>\n
<\/div>\n<\/div>\n
\n
Geom<\/em>(p<\/em>)<\/div>\n
geometric distribution<\/div>\n
f <\/em>(k<\/em>) = p<\/em>(1-p<\/em>) k<\/sup><\/em><\/div>\n
<\/div>\n<\/div>\n
\n
HG<\/em>(N<\/em>,K<\/em>,n<\/em>)<\/div>\n
hyper-geometric distribution<\/div>\n
<\/div>\n
<\/div>\n<\/div>\n
\n
Bern<\/em>(p<\/em>)<\/div>\n
Bernoulli distribution<\/div>\n
<\/div>\n
<\/div>\n<\/div>\n<\/div>\n

 
\n <\/p>\n

Combinatorics Symbols<\/h2>\n

 <\/p>\n

\n
\n
Symbol<\/strong><\/div>\n
Symbol Name<\/strong><\/div>\n
Meaning \/ definition<\/strong><\/div>\n
Example<\/strong><\/div>\n<\/div>\n
\n
n<\/em>!<\/div>\n
factorial<\/div>\n
n<\/em>! = 1\u00b72\u00b73\u00b7…\u00b7n<\/em><\/div>\n
5! = 1\u00b72\u00b73\u00b74\u00b75 = 120<\/div>\n<\/div>\n
\n
n<\/sub>Pk<\/sub><\/em><\/div>\n
permutation<\/div>\n
\"_{n}P_{k}=\\frac{n!}{(n-k)!}\"<\/div>\n
5<\/sub>P<\/em>3<\/sub> = <\/em>5! \/ (5-3)! = 60<\/div>\n<\/div>\n
\n
n<\/sub>Ck<\/sub><\/em><\/p>\n

\"\"<\/p>\n<\/div>\n

combination<\/div>\n
\"_{n}C_{k}=\\binom{n}{k}=\\frac{n!}{k!(n-k)!}\"<\/div>\n
5<\/sub>C<\/em>3<\/sub> = <\/em>5!\/[3!(5-3)!]=10<\/div>\n<\/div>\n<\/div>\n

 <\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Probability Symbols table   Symbol Symbol Name Meaning \/ definition Example P(A) probability function probability of event A P(A) = 0.5 P(A \u2229 B) probability of events intersection probability that… <\/p>\n","protected":false},"author":1,"featured_media":3121,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[34],"tags":[],"aioseo_notices":[],"amp_enabled":true,"_links":{"self":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts\/2299"}],"collection":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/comments?post=2299"}],"version-history":[{"count":7,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts\/2299\/revisions"}],"predecessor-version":[{"id":3529,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts\/2299\/revisions\/3529"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/media\/3121"}],"wp:attachment":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/media?parent=2299"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/categories?post=2299"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/tags?post=2299"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}