I hope someone can help me understand functions of random variables:(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Probability distribution of function of continuous random variables

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