From 52592c2ffead14ad7cb2e06064dcabde0ab4125f Mon Sep 17 00:00:00 2001 From: lomna-dev Date: Sun, 13 Aug 2023 18:25:02 +0530 Subject: [PATCH] Final commit for now --- main.org | 9 ++++++--- main.pdf | Bin 599027 -> 587133 bytes sampling.pdf | Bin 0 -> 202745 bytes 3 files changed, 6 insertions(+), 3 deletions(-) create mode 100644 sampling.pdf diff --git a/main.org b/main.org index e41abfe..b8d3f3b 100644 --- a/main.org +++ b/main.org @@ -414,9 +414,9 @@ To get probability from a to b (inclusive and exclusive doesn't matter in contin \[ E(X + Y) = E(X) + E(Y) \] + Variance -If +Variance is \[ V(X) = E(X^2) - (E(X))^2 \] -Then +Properties of variance are \[ V(aX) = a^2 V(X) \] \[ V(a) = 0 \] @@ -436,7 +436,6 @@ The moment generating function is given by \[ E(X^n) = (\frac{d^n}{dt^n} M(t))_{t=0} \] - * Binomial Distribution The use of a binomial distribution is to calculate a known probability repeated n number of times, i.e, doing *n* number of trials. A binomial distribution deals with discrete random variables. @@ -733,3 +732,7 @@ Here \sigma is standard deviation. + If $\rho = 0$ then $\theta = \frac{\pi}{2}$ + If $\rho = \pm 1$ then $\theta = 0$ + +TODO : Maybe an example here +* Sampling +Notes not made for this currently, a pdf was provided by teacher as, [[./sampling.pdf][./sampling.pdf]] diff --git a/main.pdf b/main.pdf index f96aefe369008e42642ab5c270aa99f98b27f938..638ad7844b5da6ad72aa4fe275c8fce7acf0263e 100644 GIT binary patch delta 136049 zcmZU(V{m5C)-BwzjgDkH<_S{SHYB!N$UtV1NnasLMESaG~~`tKUe0KS{@_CKQ z@}6q&5Ai6V+t#OyrY8Qr-*FfAZz`BAT$;0h4P4!_C)V)s=uH2(kE+XHk%bRQXS^~e z+rP)im=#LOI0~huZ5(2H%Lc5nOzW#!mJFF(Kd;~6+eV|jE@9Yu`7y(+fO56B8$VzK z3#F(vs=eN`{f|->$-~v-V4d`2FN1&=1rtUfPf4(6teDkcn`#DIpcGcY=3=Lr44&k^ zeaOliC@r;4C8vg3(O|e;wxE<+Vy>Oz<#w-45YiJ&Ff`x*oeYzNX7o$5tPvSjMSaHa z>;f*~t~@95uh;`O6vZrrb)r$H7fpFJQ9BG(;PFT#pPZ)uVE6Q@1@<~;vRJGsDfFndp=m@E{ogxw*wz{z)b zI;%cV(^{EbP`R!-x8aCFZhSE_yY2{)o#1a6=WZ&lwUV{NHXdv~G>g^6>#J8?SkdE` 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