Probability

Let X,Y,Z be three independent (i.e. mutually independent) random variables, each uniformly distributed on the interval [0,1].
1. Find the mean and variance of 1/(Z+1).
E[1/(Z+1)]=
var(1/(Z+1))=
2. Find the mean of XY/(Z+1).
Hint: Use your answer to the previous part, together with the independence assumption.
E[XY/(Z+1)]=
3. Find the probability that XY/Z≤1. Enter a numerical answer.
P(XY/Z≤1)=

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  1. 1.
    E[1/(Z+1)] = 1/2
    var(1/(Z+1)) = 0.0195
    2.
    E[XY/(Z+1)] = 0.1733
    3.
    P(XY/Z≤1) = 0.75

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  2. 1. ln(2)
    2. 0.5+ln(2)^2
    3. 0.5^2*ln(2)

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  3. Anyone care to share the rest of the answers to the test here?

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