1- A population distribution has a mean of 10 and a variance of 16. Determine the mean and variance of(Ῡ) from an i.i.d. sample from this population for (a) n=10; (b) n=100; (c) n=1000. Relate your answers to the law of large numbers.
2-Compute the following probabilities:
a. If Y is distributed N(1,4), find Pr(Y≤ 3)
b. If Y is distributed N(3,9), find Pr(Y> 0)
c. If Y is distributed N(50,25), find Pr(40 ≤ Y≤52).
d. If Y is distributed N(5,2), find Pr (6 ≤ Y ≤ 8)
3- [FONT=wf_segoe-ui_normal]In any year, the weather can inflict storm damage to a home. From year to year, the damage is random. Let Y denote the dollar value of damage in any given year. Suppose that in 95% of the years Y 50, but in 5% of the years $20,000.
thanks,
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2-Compute the following probabilities:
a. If Y is distributed N(1,4), find Pr(Y≤ 3)
b. If Y is distributed N(3,9), find Pr(Y> 0)
c. If Y is distributed N(50,25), find Pr(40 ≤ Y≤52).
d. If Y is distributed N(5,2), find Pr (6 ≤ Y ≤ 8)
3- [FONT=wf_segoe-ui_normal]In any year, the weather can inflict storm damage to a home. From year to year, the damage is random. Let Y denote the dollar value of damage in any given year. Suppose that in 95% of the years Y 50, but in 5% of the years $20,000.
thanks,
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