(a) Give a definition of a closed set. (b) Show, directly from the definition, that a...

(a) Give a definition of a closed set.

(b) Show, directly from the definition, that a union of finitely many closed sets is closed.

(c) Give an example of a countable collection of closed intervals In such that ∪ n=1 to ∞ I_n is open (make sure to prove it).

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Colby Messinger answered 2 years ago

(a) Give the definition of memoryless for a random variable X. (b) Show that if X...

(a) Give the definition of memoryless for a random variable X. (b) Show that if X is an exponential random variable with parameter λ , then X is memoryless. (c) The life of the brakes on a car is exponentially distributed with mean 50,000 miles. What is that probability that a car gets at least 70,000 miles from a set of brakes if it already has 50,000 miles?

Problem 6. Show that a closed set is a Gδ and open set is Fδ.

Suppose A and B are closed subsets of R. Show that A ∩ B and A...

Suppose A and B are closed subsets of R. Show that A ∩ B and A ∪ B are closed.

(a) Give an example of a collection of closed sets whose union is not closed. (b)...

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Consider the integers from 1 to 10. Give the set of pairs (a, b) that corresponds...

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