Question: 1. Consider the following discrete random variable X with the probability distribution given below: | P(X =x) 1 w.2 2 0.5 Bi Os Calculate the

1. Consider the following discrete random variable X with the probability distribution given below: | P(X =x) 1 w.2 2 0.5 Bi Os Calculate the expected value E|X] of the random variable X. 2. Suppose you have a population with an unknown distribution that has an expected value of E|.D| = 50 and a standard deviation of ay = 10. You draw a sample of size n = 100 from this population. According to the Central Limit Theorem, what is the expected distribution of the sample mean E|s|? 3. A factory produces light bulbs that have lifetimes following a distribution with E[D| = op = SOU hours. If you take a sample of 100 light bulbs, what is the probability that their average lifetime F|s| is between 720 and S80) hours

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