Question

Find the variance of a discrete random variable X - the number of occurrences of event A in four independent tests, if the probability of occurrence of event A in each test is 0.1. Write in the form of a table the law of distribution of the random variable X

Answer 1

$P(X=0)=(1-0.1)^4=0.6561.$

$P(X=1)=C_4^10.1(1-0.1)^3=0.2916.$

$P(X=2)=C_4^20.1^2(1-0.1)^2=0.0486.$

$P(X=3)=C_4^30.1^3(1-0.1)=0.0036.$

$P(X=4)=0.1^4=0.0001,$

The law of distribution:

$\begin{matrix} x & | &0&1&2&3&4\\ P(x) & |&0.6561&0.2916&0.0486&0.0036&0.0001 \end{matrix}$

Mean: $\mu=0.6561*0+0.2916*1+0.0486*2+0.0036*3+0.0001*4=0.4.$

Variance: $\sigma^2=0.6561*0^2+0.2916*1^2+0.0486*2^2+0.0036*3^2+0.0001*4^2-0.4^2=0.36.$