Question: Let X have EXP(1) distribution. Moreover, let Y = [X] be the integer part of X, and let Z be the integer nearest to X.

Let X have EXP(1) distribution. Moreover, let Y = [X] be the integer part of X, and let Z be the integer nearest to X. Find: (i) The distributions of Y and Z.

(ii) P(Y = Z). (iii) P(Y = 3|Z = 4). (iv) P(Z = 4|Y = 3). (v) P(Y = 4|Z = 3).

(vi) P(Z = 3|Y = 4).

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