Discussion Overview
The discussion revolves around finding the values of variables \(a\) and \(b\) in a probability distribution of a discrete random variable \(X\). Participants explore the implications of the expected value \(E[X]\) being set to both 1 and 1.5, and how these conditions relate to the probabilities assigned to different outcomes of \(X\).
Discussion Character
- Mathematical reasoning, Debate/contested
Main Points Raised
- Some participants propose that if \(E[X] = 1\), then \(a + b = 0.6\) based on the probabilities summing to 1.
- Others argue that with \(E[X] = 1.5\), a second equation can be derived, leading to a system of equations: \(a + b = 0.6\) and \(a + 3b = 0.9\).
- A later reply questions how to derive specific values for \(a\) and \(b\) from the equations, leading to a proposed solution of \(a = 0.45\) and \(b = 0.15\).
- Some participants express uncertainty about the original probability distribution table, which is referenced but not provided, leading to discussions about reconstructing it from the comments.
Areas of Agreement / Disagreement
Participants generally agree on the equations derived from the expected value conditions, but there is no consensus on the specific values of \(a\) and \(b\) until later posts. The original probability distribution table remains unclear, leading to further speculation.
Contextual Notes
The discussion lacks the original table of probabilities, which is essential for fully understanding the context of the problem. Additionally, there are unresolved assumptions regarding the values of \(a\) and \(b\) and how they relate to the probabilities assigned to \(X\).