I hope someone can help me understand functions of random variables: If X~Uniform(A,B), A < X < B Y~Normal(0,1), -inf < Y < inf and Z = X + Y - what is the pdf of Z? - how can I calculate a probability like P(Z < 3)? - what is the conditional probability P(Z<z | X = x)? - what is the conditional pdf of Z given X = x? Any hint will be appreciated. Thank you.