11 The random variable \(X\) takes the value 1 with probability \(p\) and the value 0 with probability \(1 - p\).
- Find each of the following.
- \(\mathrm { E } ( X )\)
- \(\operatorname { Var } ( X )\)
- The random variable \(Y \sim \mathrm {~B} ( 50,0.2 )\) has mean \(\mu\) and variance \(\sigma ^ { 2 }\).
Use the results of part (a) to prove that
- \(\mu = 10\)
- \(\sigma ^ { 2 } = 8\).