Given: X is a random variable, $E|X|^\alpha<\infty$ with some $\alpha>0$ Prove that $E|X+b|^\alpha < \infty$ for any real b. Prove that $E|X+b|^\alpha = \infty$ if b-> $\infty$ My suggestion is triangle inequality: $E|X+b|^\alpha\leq E|X|^\alpha + E|b|^\alpha$ but I can`t prove it myself, any thoughts?
2026-02-24 05:04:07.1771909447
Mathematical expectation problem
60 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in CALCULUS
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