Consider the sample space S = [0, 1] with a probability measure that is uniform on this space, i.e. P([a, b) = b – a, for all 0 < a < b < 1. Define the sequence {X,,n = 1, 2, · .} as follows: ... n+1 2n 1 X,(s) = otherwise Also, define the random variable X on this sample space as follows: 1 0
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![Consider the sample space S = [0, 1] with a probability measure that is uniform on this space, i.e,
Р(а, b) — ь - а,
for all 0 < a < b < 1.
Define the sequence {Xn,n = 1, 2, · · · } as follows:
...
n+1
2n
1
X,(s) =
otherwise
Also, define the random variable X on this sample space as follows:
1
0<s<
X(s) =
otherwise
a.s.
Show that X,
→ x.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1683420b-4b84-4b56-ab71-03868277ba57%2F83fef62d-744f-4a09-9b14-c6d2b53af704%2F6luvygu_processed.jpeg&w=3840&q=75)
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