Question: 1.*5. Let .:'7>(Xl = 2n) = 1j2n, n :::: 1; and let {Xn, n :::: I} be independent and identically distributed. Show that the weak

1.*5. Let .:'7>(Xl = 2n) = 1j2n, n :::: 1; and let {Xn, n :::: I} be independent and identically distributed. Show that the weak law of large numbers does not hold for bll

= 11; namely, with this choice of bn no sequence {an} exists for which (6) is true. [This is the St. Petersburg paradox, in which you win 2n if it takes 11 tosses of a coin to obtain a head. What would you consider as a fair entry fee? and what is your mathematical expectation?]

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