Question: Please refer to the problem below, thanks! Consider the sequence of binary random variables Consider the sequence of binary random variables {{, |~_, satisfying the

Please refer to the problem below, thanks!

Consider the sequence of binary random variables

Consider the sequence of binary random variables {{, |~_, satisfying the following properties (a)*` E |O , 61 for all A , where b is some positive real number . ibj for any fixed WE Al, the deterministic sequence*, lo'! has the property that for any integer &_ !` I* - [^ ^ ; ( @0 ) = 6 , i.e. there is precisely one nonzero element of the sequence ( I, I'w'!' that takes on the value b within the interval | 2, 2* + 1 . ... 2471 _ 1] for any &_ O and all ?" possibilities are equally likely . ( a) Identify the values of' 6 ( if any ; for which this sequence converges in probability . Ibj Identify the values of ! ( if any ; for which this sequence converges in the mean square . ( C ) Identify the values of 6 ( if any ; for which this sequence converges almost surely . Explain fully , your answers

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