Question

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.

Answer #1

Let the sum of of two uniform distributed variables given
be

Y = X_{1} + X_{2}

The CDF for Y here is obtained as:

P( Y <= y)

= P( X_{1} + X_{2} <= y)

= P( X_{1} <= y - x_{2})

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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