The random variable​ X, representing the number of errors per 100 lines of software​ code, has the following probability distribution. x 2 3 4 5 6 ​f(x) 0.25 0.4 0.04 0.01 0.3 Use the following theorem to determine the variance of the random variable X. The variance of a random variable X is sigma squared equals Upper E (Upper X squared )minus mu squared.

Answer:10.4205Step-by-step explanation:Let's find first the Expectation of the random variable X, E(X) The Expectation of X has the following formula [tex]\large E(X)=\sum x_kp(x_k)[/tex] where [tex]\large x_k[/tex] values of the discrete random variable [tex]\large p(x_k)[/tex] probabilities of the values  [tex]\large E(X)=2*0.25+3*0.4+4*0.04+5*0.01+6*0.3=\bf 3.71[/tex] To determine the variance of the random variable X, we will use the formula [tex]\large Var(X)=E((X-E(X))^2)[/tex] So, [tex]\large Var(X)=(2-3.71)^2+(3-3.71)^2+(4-3.71)^2+(5-3.71)^2+(6-3.71)^2[/tex] and the Variance is [tex]\large \boxed{Var(X)=10.4205}[/tex]