Indicate whether the following are true or false: (a) The CDF is always non-nega
ID: 3304527 • Letter: I
Question
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.
(f) Entropy is maximum when all outcomes in the sample space have equal probability.
(g) Entropy cannot be negative.
(h) The random variables X and X – E(X) must have the same variance.
(i) The random variables X and X/E(X) must have the same variance.
(j) V AR(X + 1) = V AR(X) + 1 for all possible random variables X.
(k) V AR(-X) = -V AR(X) for some random variables X.
(l) For events, A, B, P(A) can sometimes be less than P(AÇB).
(m) For events A, B, P(A|B) cannot be more than P(A).
(n) For events A, B, P(A|B) cannot be less than P(A).
(o) The geometric random variable is memoryless
Explanation / Answer
(According to Chegg policy, only four subquestions will be answered. Please post the remaining in another question)
(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.