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

Solution:

$p=0.1,q=0.9,n=4$

$X\sim Bin(n,p) \\ Var(X)=npq=4(0.1)(0.9)=0.36$

$P(X=0)=\ ^4C_0(0.1)^0(0.9)^4=0.6561 \\ P(X=1)=\ ^4C_1(0.1)^1(0.9)^3=0.2916 \\ P(X=2)=\ ^4C_2(0.1)^2(0.9)^2=0.0486 \\ P(X=3)=\ ^4C_3(0.1)^3(0.9)^1=0.0036 \\ P(X=4)=\ ^4C_4(0.1)^4(0.9)^0=0.0001$