Each of the following statements is either True or False. Please clearly indicate True or False...

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Each of the following statements is either True or False. Please clearly indicate True or False in the below. All questions have equal weight. Consider a probabilistic model with a sample space 2, a collection of events that are subsets of 2, and a probability law P() defined on the collection of events-all exactly as usual. Let A, B and C be events. (a) If P(A) < P(B), then A C B. (T/F) (b) If A CB then P(A) < P(B). (T/F) (c) Assuming P(B) > 0, P(A|B) is at least as large as P(A). (T/F) Let X be an exponentially distributed random variable with a probability density function fx (x) = e-*. (d) If P({0 < X < 3} U P{0 < X < 3}) = 1-e-4. (T/F) Each of the following statements is either True or False. Please clearly indicate True or False in the below. All questions have equal weight. Consider a probabilistic model with a sample space 2, a collection of events that are subsets of 2, and a probability law P() defined on the collection of events-all exactly as usual. Let A, B and C be events. (a) If P(A) < P(B), then A C B. (T/F) (b) If A CB then P(A) < P(B). (T/F) (c) Assuming P(B) > 0, P(A|B) is at least as large as P(A). (T/F) Let X be an exponentially distributed random variable with a probability density function fx (x) = e-*. (d) If P({0 < X < 3} U P{0 < X < 3}) = 1-e-4. (T/F)