Question

A certain student has missed several weeks of class. This same student takes an exam comprised of 10 multiple choice questions. Each multiple choice question has 5 different choices. Assume further that this student has no knowledge of the material and takes a wild guess on each question.
What is the variance for how many he will get correct on this exam?

Answer 1

P(right answer) = 1/5

Ex- math expectation = $\sum_{i=1}^{10} i * \left(\frac{1}{5}\right)^i = 0.31$

Ex² = $\sum_{i=1}^{10} i^2 * \left(\frac{1}{5}\right)^i = 0.47$

Dx- variance = Ex² - (Ex)^2 = 0.47 - 0.1 = 0.37