# SOLUTION: Help me,,, Given &#8747;_A&#9618;&#12310;[1/&#960;(1+x^2 ) ] dx&#12311;, where A &#8834; "A" = {x : -&#8734; < x < &#8734;}. Show that the integral could serve as a probability

Algebra ->  Algebra  -> Probability-and-statistics -> SOLUTION: Help me,,, Given &#8747;_A&#9618;&#12310;[1/&#960;(1+x^2 ) ] dx&#12311;, where A &#8834; "A" = {x : -&#8734; < x < &#8734;}. Show that the integral could serve as a probability      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Algebra: Probability and statistics Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Probability-and-statistics 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(4012)   (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.