hi, can you help me solve this question? Let X be a (real-valued) random variable. We define the law of XLx(B) :3 P(X"(В)) — P(w € N: X(u) € В),for all (Borel) sets BE B(R), to be the distribution of X. Prove that Lx is a probabilitymeasure on B(R).

X is a real-valued random variable. The law of X is defined as follows. for all, Borel sets to be…

Let X be a (real-valued) random variable. We define the law of X Lx(B) := P(X¯¹(B)) = P(w ≤ N : X(w) Є B), for all (Borel) sets B = B(R), to be the distribution of X. Prove that Lx is a probability measure on B(R).

Let X be a (real-valued) random variable. We define the law of X Lx(B) := P(X¯¹(B)) = P(w ≤ N : X(w) Є B), for all (Borel) sets B = B(R), to be the distribution of X. Prove that Lx is a probability measure on B(R).

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

hi, can you help me solve this question?

Let X be a (real-valued) random variable. We define the law of X
Lx(B) :3 P(X"(В)) — P(w € N: X(u) € В),
for all (Borel) sets BE B(R), to be the distribution of X. Prove that Lx is a probability
measure on B(R).

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