Probability density function
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) Let X and Y have joint probability density function f(x,y) (s,t) = ce ^ -(s + 2t) for
0 <= s, and 0 <= t. Find
(a) c
(b) Pr {min (X, Y) 1/3}
(c) Pr {X <= Y}
(d) The marginal probability density function of X
(e) E [XY]
5) Let X and Y be independent uniform (0,1) random variables. Compute
(a) Pr {X < Y}
(b) Pr {X = Y}
(c) The probability density function of X + Y
(d) Var[X]
(e) Var[X + Y]
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Solution Summary
Given a joint density function, this shows how to compute a marginal probability density function; given the type of variable, this shows how to compute probability density function.
Solution Preview
1)
a) We must have:
Therefore:
c=2.
b) I think that must be Pr{min(X, Y)<=1/3}. Then:
c) Pr{X<=Y}:
There are two methods for solving this problem.
Method 1:
Method 2:
remember that s represents X and t represents Y.
d) The ...
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