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I am stuck with this problem... Please help!

Define the rounding function [.] to integers as follows:

[x] = j if x ∈ (j-0.5, j+0.5, for j = 0,+-1, +-2,...

Suppose X has a uniform distribution on the interval (a,b). i.e., X~U(a,b) a<b.

1. find a pair a and b such hat Var(X) > Var([X]) and such that VAR(X) < VAR([X])

2. Suppose that a random variable X has a continuous CDF F(x). What are the distributions of F(X) and [F(X)]? and finally R = [F(X)]-F(X)?

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# Statistical Inference Question

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