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Suppose X~N(0,s), and Y is a random variable that has a probability mass point at 0 but is otherwise uniformally distributed on (0,t] so that:

f(y)=k, y=0

f(y)=(1-k)(1/t), 0 < y < t

f(y)=0 otherwise

What is

Pr(y < A | x + y > B)

where A and B are arbitrary constants?

I think I've calculated the convolution of X and Y, but I'm not sure how to get the density from there (and I'm not sure I have the convolution right either). Thanks for any help you can provide.