| Front | What is the expected value of a random variable? |
| Back | If [$]R[/$] is a random variable defined on a sample space [$]S[/$], the expected value of [$]R[/$] is [$]\mathbf{E}[R]=\sum_{w \in S} R(w) \cdot \Pr[w][/$]Alternate definition: If [$]R[/$] is a random variable defined on a sample space [$]S[/$], then [$]\mathbf{E}[R] = \sum_{x \in \text{range}(R)} x \cdot \Pr[R=x][/$] |
| Tags | Courses_MathematicsForComputerScience_Chapter18 Maths Probability |
| Front | In probability, what is the sum rule? |
| Back | If [$]\{E_0, E_1, \dotsc\}[/$] is a collection of disjoint events, then [$]\Pr[\cup_{n \in \mathbb{N}} E_n] = \sum_{n \in \mathbb{N}} \Pr[E_n][/$] |
| Tags | Courses_MathematicsForComputerScience_Chapter14 Maths Probability |
| Front | What is the standard deviation of a random variable? |
| Back | The standard deviation, [$]\sigma_R[/$], of a random variable [$]R[/$] is [$]\sqrt{\text{Var}[R]}[/$]. Also known as the root mean square |
| Tags | Courses_MathematicsForComputerScience_Chapter19 Maths |