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## Main Question or Discussion Point

Hi Guys.

I'm trying to understand how to solve the following problem. Any help and explanation would be greatly appreciated!

thanks.

Let X and Y be independent N(0, 1) random variables and let Z = X + Y.

What is the distribution of Z? Write down the density function of Z.

Also:

Show that E[Z|X > 0, Y > 0] = 2

I'm trying to understand how to solve the following problem. Any help and explanation would be greatly appreciated!

thanks.

Let X and Y be independent N(0, 1) random variables and let Z = X + Y.

What is the distribution of Z? Write down the density function of Z.

Also:

Show that E[Z|X > 0, Y > 0] = 2