Is this answer correct Let X denote a random variable that t

Let X denote a random variable that takes on any of the values -1, 0, and 1 with respective probabilities Calculate Var(X) if X represents the outcome when a fair die is rolled. It is known that screws produced by a certain company will be defective with probability .01, each other The company sells the screws in packages of 10 and offers a money-back guarantee that at most 1 of the 10 screws is defective. What proportion of packages sold must the company replace?

Solution

1) Answer is wrong. the correct answer is as follows:

E(X²) = (-1²)*(0.2) +(0²)*(0.5) +(1²)*(0.3) = 0.2 + 0 + 0.3 = 0.5

2) E(X) is correct

V(X) = E(X²) - (E(X))² = (1+4+9+16+25+36)/6 -(3.5)² =2.9167