Probability Distributions - Important Formulas

Dear students, before you start revision for the chapter Probability Distributions, first make sure you revise all the formulas and key points. Only if you are thorough with the main concepts and formulas, you can confidently work out all the sums. That said, here are the most important formulas in Lesson 7 Probability Distributions , Class 12 Business Maths.

Binomial Distribution

$P(X=x)=p(x)=nC_{x}p^{x}q^{n-x}\; where\; x=1,2,3....n \\$
$p+q=1 \\$
$Mean=np \\$
$Variance=npq \\$
$\text{In binomial distribution,}\; variance < mean\\$
$S.D=\sqrt{npq} \\$

Poisson Distribution

$p(x)=\dfrac{e^{-\lambda}\; \lambda^{x}}{x!}\; x=0,1,2,3....\\$
$Mean=\lambda \\$
$Variance = \lambda \\$
$\text{Poisson distribution is the only distribution in which the.} \\$
$\text{mean and variance are equal.} \\$

Normal Distribution

$f(x: \mu,\sigma )=)=\frac{1}{\sigma\; \sqrt{2 \pi}}exp\; \\$
$\left\{ {\frac{-1}{2}} \left( \frac{x- \mu}{\sigma} \right)^{2} \right\} \\$
$Mean = \mu \\$
$Variance = \sigma^{2} \\$
$S.D = \sigma \\$
$p(-\infty < z < 0)=0.5 \\$
$p(0 < z < \infty)=0.5 \\$
$p(-\infty < z < \infty)=1 \\$
$z=\dfrac{x- \mu}{\sigma} \\$