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Probability distribution of function of continuous random variables

  1. Oct 17, 2004 #1
    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.
  2. jcsd
  3. Oct 17, 2004 #2
    What have u tried for 1?

    -- AI
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