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I am trying to understand the following proof: enter image description here

enter image description here

Proof:enter image description here enter image description here

Main Confusion: In particular, I am having a very hard time understanding the chain of inequalities in the proof for (3)': I think the first equality is due to $X$ being symmetric. However, how did we obtain the rest of the inequalities? Could someone expand and explain the details behind these inequalities?

I am trying to understand the following proof: enter image description here

enter image description here

Proof: enter image description here

Main Confusion: In particular, I am having a very hard time understanding the chain of inequalities in the proof: I think the first equality is due to $X$ being symmetric. However, how did we obtain the rest of the inequalities? Could someone expand and explain the details behind these inequalities?

I am trying to understand the following proof: enter image description here

enter image description here

enter image description here enter image description here

Main Confusion: In particular, I am having a very hard time understanding the chain of inequalities in the proof for (3)': I think the first equality is due to $X$ being symmetric. However, how did we obtain the rest of the inequalities? Could someone expand and explain the details behind these inequalities?

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Partial T
Partial T
  • 593
  • 2
  • 13

Centered Subgaussian Variables have better Properties

I am trying to understand the following proof: enter image description here

enter image description here

Proof: enter image description here

Main Confusion: In particular, I am having a very hard time understanding the chain of inequalities in the proof: I think the first equality is due to $X$ being symmetric. However, how did we obtain the rest of the inequalities? Could someone expand and explain the details behind these inequalities?