SOLUTION: Help me,,,
Given ∫_A▒〖[1/π(1+x^2 ) ] dx〗, where A ⊂ "A" = {x : -∞ < x < ∞}. Show that the integral could serve as a probability
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Question 460395: Help me,,,
Given ∫_A▒〖[1/π(1+x^2 ) ] dx〗, where A ⊂ "A" = {x : -∞ < x < ∞}. Show that the integral could serve as a probability set function of a random variable X whose space is "A" .
Let the probability set function of the random variable X be
P(A) = ∫_A▒〖e^(-x) dx,〗 where "A" = {x : 0 < x < ∞}.
Let Ak = {x : 2 – 1/k < x ≤3}, k = 1, 2, 3,….. Find lim┬(k→∞)〖A_k 〗 and P(lim┬(k→∞)〖A_k 〗).
Find P(Ak) and 〖lim┬(k→∞) P(〗〖A_k 〗). Note that 〖lim┬(k→∞) P(〗〖A_k 〗) = P(lim┬(k→∞)〖A_k 〗).
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
There's a bit of a problem in the third question. You have defined the set but have not defined the function OVER THAT SET. The density function has to be dependent also on k OVER THAT SET for the questions to be answered.
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