document.write( "Question 460395: Help me,,,
\n" ); document.write( "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\" .
\n" ); document.write( " Let the probability set function of the random variable X be
\n" ); document.write( "P(A) = ∫_A▒〖e^(-x) dx,〗 where \"A\" = {x : 0 < x < ∞}.
\n" ); document.write( "Let Ak = {x : 2 – 1/k < x ≤3}, k = 1, 2, 3,….. Find lim┬(k→∞)⁡〖A_k 〗 and P(lim┬(k→∞)⁡〖A_k 〗).
\n" ); document.write( "Find P(Ak) and 〖lim┬(k→∞) P(〗⁡〖A_k 〗). Note that 〖lim┬(k→∞) P(〗⁡〖A_k 〗) = P(lim┬(k→∞)⁡〖A_k 〗). \n" ); document.write( "
Algebra.Com's Answer #315774 by robertb(5830)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "There's a bit of a problem in the third question. You have defined the set \"A%5Bk%5D\" 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. \n" ); document.write( "
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