Is one-sided standard normal a sub-gaussian? [duplicate]

For example, does the positive part of the standard normal distribution satisfy sub-gaussian property?

• $P(\vert X \vert >t)$ is the same for standard normal and one-sided standard normal. Commented Jun 12, 2018 at 18:28
• I agree with you. One way of checking the sub-gaussianity by showing the moment generating function of that r.v. is upper bounded by exponential quantity. How do I establish the same for one-sided standard r.v. While doing that, I'm encountering an additional multiplier 2. I'm not sure how to get rid of it. Hope my question is clear. Commented Jun 12, 2018 at 19:13
• This question is a simple special case of your subsequent question.
– whuber
Commented Jun 12, 2018 at 19:52
• I don't think that the multiplier matters for sub-gaussianity. But anyway, the multiplier 2 happens in both cases. The normal distribution has two tails (negative - positive) the half normal distribution tail is twice as high, but there is only one tail. Commented Jun 13, 2018 at 8:01