Please answer all parts if confident 2 (15) Indicate whether the following are t

Question

Please answer all parts if confident

2 (15) Indicate whether the following are true or false: (a) The CDF is always non-negative. (b) The PDF is always non-negative. (c) The value of the CDF can never be greater than 1 (d) The CDF is always non-decreasing (e) The PDF is always non-decreasing. Entropy is maximum when all outcomes in the sample space have equal probability (g) Entropy cannot be negative. The random variables X and X- ECX) must have the same variance. The random variables X and X/ECA) must have the same variance. ) VARX+)- VAR)+ I for all possible random variables N (k) VAR(X)--VAR(X) for some random variables X. (1) For events, A, B, P(4) can sometimes be less than PlAnB). )For events A, B, PUAB) cannot be more than Pa). (n) For events A, B, P(4|B) cannot be less than P(A). (o) The geometric random variable is memoryless

Explanation / Answer

(a) The CDF is always non-negative. -> False.

(b) The PDF is always non-negative. -> True.

(c) The value of the CDF can never be greater than 1. -> True.

(d) The CDF is always non-decreasing. -> True.

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