Let X have a uniform distribution on the interval (4, 8). Find the probability that the sum of 2 independent observations of X is greater than 13.
Let the sum of of two uniform distributed variables given
be
Y = X1 + X2
The CDF for Y here is obtained as:
P( Y <= y)
= P( X1 + X2 <= y)
= P( X1 <= y - x2)
Now the probability that the sum is greater than 13 is computed here as:
= 1 - P( Y <= 13)
= 1 - (13 - 10) / 4
= 1 - (3/4)
= 1 - 0.75 = 0.25
Therefore 0.25 is the required probability here.
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