The psi-2 norm of a Rademacher sign

NumericalBeginner⏱ 15 minHigh-Dim Probabilityrademacherorliczbounded

Theory: Sub-Gaussian and Sub-Exponential Random Variables →

Problem

Compute $\|\eps\|_{\psi_2}$ for a Rademacher sign $\eps\in\{-1,+1\}$ , and more generally show that any $X$ with $|X|\le M$ almost surely satisfies $\|X\|_{\psi_2}\le M/\sqrt{\log2}$ .

Compute the requested quantities and say what they mean. A number without an interpretation is not an answer.

Hints

Hints — 0 of 2 revealed

Solution

Opening this before you have a real attempt on paper is the fastest way to feel like you understand something you cannot reproduce.

Related problems

All problems

Problem	Field	Type	Difficulty	Time
A variable with all moments finite that is not sub-Gaussian	High-Dim Probability	Proof	Intermediate	30 min
The psi-2 norm of a Gaussian	High-Dim Probability	Numerical	Intermediate	15 min
From moment growth to a tail bound	High-Dim Probability	Proof	Advanced	1 hour
Massart's finite maximal inequality	Learning Theory	Proof	Advanced	30 min
Products of sub-Gaussians are sub-exponential	High-Dim Probability	Proof	Advanced	30 min