Question: 8.47 Consider the probability space (,T,P) with =[0,1],T defined to be the Borel sets of , and for 0 <1.(a) Show that P[{0}]=0 by using

8.47 Consider the probability space (,T,P) with =[0,1],T defined to be the Borel sets of , and for 0<1.(a) Show that P[{0}]=0 by using the axioms of probability.(b) Determine in what senses the following random sequences converge:(i)x[n,]=e-n,n0(ii)x[n,]=sin(1n),n1(iii)x[n,]=cosn(),n0.

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