Find P(X$\boldsymbol{\lt}$4) ,P(3$\boldsymbol{\lt}$X$\boldsymbol{\lt}$6)

Mumbai University > Mechanical Engineering > Sem 4 > Applied Mathematics IV

Marks: 6M

Year: Dec 2015

We know that, total probability is always equal to 1.

$\mathrm{\therefore } \sum{P_i} = 1$

$\mathrm{\therefore } k+3k+5k +7k+9k+11k +13k = 1$

$\mathrm{\therefore }$ 49k = 1

$\mathrm{\therefore }$ k = 1/49

Probability density function becomes:

To find : P(X$\lt$4) $P(X < 4) = P(X=0)+P(X=1)+P(X=2)+P(X=3)$ $= 1/49+3/49+5/49 +1/7 = 16/49$ To find: P(3$<$X$\lt$6)< p="">

$P(3 \lt X \lt 6) = P(X = 4) + P(X = 5)$

$= 9/49 + 11/49$

$= 20/49$