Some Important formula on Random Variable

Hi, I am writing here some important formula which will be very useful when you solve GATE questions. I am not giving you the derivation because derivations are not important for the Gate. If you are interested in derivations please refer  to a book by Mr. Ross Sheldon


1. Discrete random variable:

  1. Mean         \left ( \mu \right )=\sum (x).f\left ( x \right )
  2. Varience(\sigma ^{2})= x^{2}.f\left ( x \right ) -(x.f(x))^{2}
  3. S.D                      =  \sqrt{varience}

2. Bionomial Distribution:-

  • Mean          (\mu) =np
  • Variance  (\sigma ^{^{2}})= npq
  • S.D.                      = \sqrt{npq}


3.Poisson distribution:-

  • P(Y=i)= e^{^{^{-\lambda }}} \lambda ^{^{i}}/i ! 
  • Variance = \lambda
  • \lambda =np   //in case if n is very large and p is very small.
  • mean= variance
  • V(ax\pm by)= a^{2 } V(x) \pm b^{2}V(y)
  • Variance can't be negative.


  • n= no. of trials
  • p= probability of success
  • q= probability if failure = 1-p
  • e=2.71828