Answer:
Option B) 0.63
Step-by-step explanation:
We are given the following in the question:
X: 0 1 2 3
P(x): 0.027 0.189 0.441 0.343
We have to find the variance for the given discrete probability distribution.
[tex]E(X) = \displaystyle\sum x_iP(x_i)\\\\E(X) = 0(0.027) + 1(0.189) + 2(0.441) + 3(0.343)\\E(X) = 2.1\\\\E(X^2) = \displaystyle\sum x_i^2P(x_i)\\\\E(X^2) = 0^2(0.027) + 1^2(0.189) + 2^2(0.441) + 3^2(0.343)\\E(X^2) = 5.04\\\\Var(X) = E(X^2) -[E(X)]^2\\Var(X) = 5.04 - (2.1)^2\\Var(X) = 0.63[/tex]
The variance of given distribution is 0.63
