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257.1357 603.2765 Tm (i)Tj /F3 1 Tf 11.9552 0 0 11.9552 263.7729 605.0697 Tm ()Tj /F2 1 Tf 1.0636 0 TD ()Tj /F4 1 Tf -0.0636 0 TD (x)Tj /F2 1 Tf 0.5715 0 TD (\))Tj /F6 1 Tf 8.3686 0 0 8.3686 287.21 609.4084 Tm (2)Tj /F4 1 Tf 11.9552 0 0 11.9552 292.5728 605.0697 Tm (f)Tj /F5 1 Tf 8.3686 0 0 8.3686 298.4259 603.2765 Tm (i)Tj ET 245.61 600.268 56.752 -0.478 re f BT /F4 1 Tf 11.9552 0 0 11.9552 270.4428 588.7808 Tm (n)Tj /F2 1 Tf 3.0714 0.686 TD (=)Tj /F8 1 Tf 1.0555 0.95 TD ()Tj /F2 1 Tf 1.4445 -0.95 TD (\()Tj /F4 1 Tf 0.3888 0 TD (x)Tj /F5 1 Tf 8.3686 0 0 8.3686 348.532 595.1888 Tm (i)Tj /F3 1 Tf 11.9552 0 0 11.9552 355.1691 596.9821 Tm ()Tj /F2 1 Tf 1.0635 0 TD ()Tj /F4 1 Tf -0.0636 0 TD (x)Tj /F2 1 Tf 0.5716 0 TD (\))Tj /F6 1 Tf 8.3686 0 0 8.3686 378.6053 601.9186 Tm (2)Tj /F4 1 Tf 11.9552 0 0 11.9552 383.9691 596.9821 Tm (r)Tj /F5 1 Tf 8.3686 0 0 8.3686 389.3629 595.1888 Tm (i)Tj /F2 1 Tf 11.9552 0 0 11.9552 212.3387 571.4458 Tm (=)Tj /F8 1 Tf 1.0556 0.95 TD ()Tj /F2 1 Tf 1.4444 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Tf 0 -0.943 TD (i)Tj /F4 1 Tf 11.9552 0 0 11.9552 256.4154 547.5355 Tm (r)Tj /F5 1 Tf 8.3686 0 0 8.3686 261.8092 545.7422 Tm (i)Tj /F3 1 Tf 11.9552 0 0 11.9552 268.4463 547.5355 Tm 0.2222 Tc ({)Tj /F2 1 Tf 1.5635 0 TD 0 Tc ()Tj /F4 1 Tf -0.0635 0 TD (x)Tj /F3 1 Tf 0.5715 0 TD (})Tj /F6 1 Tf 8.3686 0 0 8.3686 299.1891 552.472 Tm (2)Tj /F4 1 Tf 11.9552 0 0 11.9552 304.5519 547.5355 Tm (,)Tj /F2 1 Tf -18.7407 -2.1452 TD [(whic)27.7(h)-290.1(follo)27.8(ws)-290.1(since)-353.7()]TJ /F4 1 Tf 8.4648 0 TD (x)Tj /F2 1 Tf 0.8617 0 TD [(is)-290.1(a)-290.1(constan)27.7(t)-290.1(that)-290.1(is)-290.2(not)-290.1(amenable)-290.2(to)-290.2(the)-290.1(a)27.8(v)27.8(eraging)-290.2(op)-27.8(eration.)]TJ /F1 1 Tf -9.3265 -1.7113 TD [(Probabilit)31.9(y)-341.7(and)-341.6(the)-341.7(limit)-341.7(of)-341.7(relativ)31.9(e)-341.7(frequency)95.8(.)]TJ /F2 1 Tf 23.7282 0 TD [(Let)-297.1(us)-297.2(consider)-297.2(an)-297.1(indenite)]TJ -23.7282 -1.2 TD [(sequence)-299(of)-299(tosses.)-433.1(W)83.4(e)-299(should)-299.1(observ)27.7(e)-299(that,)-305.9(as)]TJ /F4 1 Tf 20.4079 0 TD (n)Tj /F3 1 Tf 0.878 0 TD 0.2778 Tc ()Tj /F2 1 Tf 2.2778 0 TD 0 Tc [(,)-305.9(the)-299(relativ)27.7(e)-299.1(frequencies)-299.1(will)]TJ -23.5638 -1.2 TD [(con)27.7(v)27.8(erge)-396.6(to)-396.7(v)55.6(alues)-396.7(in)-396.7(the)-396.7(near)-396.7(neigh)27.8(b)-27.8(ourho)-27.8(o)-27.8(d)-396.6(of)-396.7(1)]TJ /F4 1 Tf 22.3817 0 TD (/)Tj /F2 1 Tf 0.5 0 TD [(6.)-634.4(W)83.3(e)-396.6(will)-396.7(recognise)-396.7(that)-396.7(the)]TJ -22.8817 -1.2 TD [(v)55.5(alue)]TJ /F4 1 Tf 2.5626 0 TD (p)Tj /F5 1 Tf 8.3686 0 0 8.3686 117.1547 456.5984 Tm (i)Tj /F2 1 Tf 11.9552 0 0 11.9552 124.4563 458.3917 Tm 0.2777 Tc (=1)Tj /F4 1 Tf 1.5555 0 TD 0 Tc (/)Tj /F2 1 Tf 0.5 0 TD [(6)-312.6(i)0(s)-312.6(the)-312.6(probabilit)27.7(y)-312.6(o)0(f)-312.6(the)-312.6(o)-27.8(ccurrence)-312.7(of)-312.6(a)-312.6(particular)-312.7(n)27.8(u)0(m)27.8(b)-27.9(er)]TJ /F4 1 Tf 26.5163 0 TD 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-1.2 TD [(after)-444.6(to)-444.7(reside)-444.6(within)-444.7(a)-444.7(limited)-444.7(neigh)27.8(b)-27.8(ourho)-27.8(o)-27.8(d)-444.7(of)]TJ /F4 1 Tf 22.6266 0 TD (p)Tj /F5 1 Tf 8.3686 0 0 8.3686 357.0241 356.1751 Tm (i)Tj /F2 1 Tf 11.9552 0 0 11.9552 361.0043 357.9683 Tm [(.)-778.4(\(Suc)27.7(h)-444.6(a)-444.7(neigh)27.7(b)-27.8(ourho)-27.8(o)-27.8(d)-444.6(is)]TJ -23.4627 -1.2 TD [(denoted)-338.5(b)27.8(y)-338.5(the)-338.5(in)27.7(terv)55.6(al)-338.5(\()]TJ /F4 1 Tf 10.9123 0 TD (p)Tj /F2 1 Tf 0.7288 0 TD (+)Tj /F4 1 Tf 1.0034 0 TD ()Tj /F5 1 Tf 8.3686 0 0 8.3686 236.523 341.8288 Tm (n)Tj /F4 1 Tf 11.9552 0 0 11.9552 243.0306 343.6221 Tm 0.1667 Tc (,p)Tj /F3 1 Tf 1.1733 0 TD 0 Tc ()Tj /F4 1 Tf 1.0034 0 TD ()Tj /F5 1 Tf 8.3686 0 0 8.3686 273.9059 341.8288 Tm (n)Tj /F2 1 Tf 11.9552 0 0 11.9552 280.4135 343.6221 Tm [(\),)-339.8(where)]TJ /F4 1 Tf 3.9032 0 TD ()Tj /F5 1 Tf 8.3686 0 0 8.3686 331.9302 341.8288 Tm (n)Tj /F2 1 Tf 11.9552 0 0 11.9552 342.4837 343.6221 Tm [(is)-338.5(a)-338.4(n)27.7(um)27.8(b)-27.8(e)0(r)-338.5(that)-338.5(gets)-338.5(smaller)-338.5(as)]TJ /F4 1 Tf -21.9135 -1.2 TD (n)Tj /F2 1 Tf 0.9336 0 TD (increases.\))Tj 1.0664 -1.2 TD [(The)-283.8(reason)-283.8(is)-283.8(that)-283.8(there)-283.8(is)-283.9(alw)27.8(a)27.7(y)0(s)-283.8(a)-283.7(w)27.7(a)27.8(yw)27.7(ard)-283.8(c)27.8(hance)-283.8(that,)-293.8(b)27.7(y)-283.7(a)-283.8(run)-283.7(of)-283.8(ab)-27.8(erran)27.7(t)]TJ -2 -1.2 TD [(outcomes,)-326.9(the)-325.2(v)55.5(alue)-325.2(of)]TJ /F4 1 Tf 10.0859 0 TD (r)Tj /F5 1 Tf 8.3686 0 0 8.3686 206.4767 298.7903 Tm (i)Tj /F2 1 Tf 11.9552 0 0 11.9552 214.3452 300.5835 Tm [(will)-325.2(break)-325.3(the)-325.3(b)-27.8(ounds)-325.3(of)-325.3(the)-325.2(neigh)27.7(b)-27.8(ourho)-27.8(o)-27.8(d)0(.)-441.8(All)-325.2(that)-325.3(w)27.7(e)]TJ -11.1953 -1.2 TD 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[(W)83.4(e)-334.6(shall)-334.6(con)27.7(tin)27.8(ue,)-334.9(for)-334.5(the)-334.5(presen)27.7(t,)-334.8(to)-334.5(assume)-334.6(that)-334.6(w)27.8(e)-334.6(understand)-334.6(unquestion-)]TJ -2 -1.2 TD [(ably)-427.3(that)-427.4(the)-427.4(probabilit)27.7(y)-427.3(o)0(f)-427.4(a)0(n)27.8(y)-427.3(n)27.7(u)0(m)27.8(b)-27.8(er)]TJ /F4 1 Tf 18.5246 0 TD (x)Tj /F5 1 Tf 8.3686 0 0 8.3686 308.802 212.713 Tm (i)Tj /F2 1 Tf 11.9552 0 0 11.9552 317.8909 214.5063 Tm [(arising)-427.3(from)-427.4(the)-427.3(toss)-427.4(of)-427.3(a)-427.3(fair)-427.4(die)-427.3(is)]TJ /F4 1 Tf -19.8564 -1.2 TD (p)Tj /F5 1 Tf 8.3686 0 0 8.3686 86.5185 198.3668 Tm (i)Tj /F2 1 Tf 11.9552 0 0 11.9552 95.8864 200.1601 Tm 0.4506 Tc (=1)Tj /F4 1 Tf 1.7284 0 TD 0 Tc (/)Tj /F2 1 Tf 0.5 0 TD [(6)-437.1(for)-437.1(all)]TJ /F4 1 Tf 4.064 0 TD (i)Tj /F2 1 Tf 0.3445 0 TD [(.)-755.6(Indeed,)-463.1(this)-437(constitutes)-437.2(our)-437.1(denition)-437.1(of)-437.1(a)-437(fair)-437.1(die.)-755.6(W)83.3(e)-437.1(can)]TJ -7.9236 -1.2 TD 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(AND.)Tj /F2 1 Tf 2.9509 0 TD [(That)-402.6(is)-402.6(to)-402.6(sa)27.8(y)-402.6(\()]TJ /F4 1 Tf 7.1216 0 TD (A)Tj /F6 1 Tf 8.3686 0 0 8.3686 407.9034 453.1534 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 416.4752 454.9467 Tm ()Tj /F4 1 Tf 0.9351 0 TD (B)Tj /F6 1 Tf 8.3686 0 0 8.3686 436.7223 453.1534 Tm (4)Tj /F2 1 Tf 11.9552 0 0 11.9552 442.0852 454.9467 Tm [(\))-402.6(means)-402.7(that)]TJ /F7 1 Tf -30.2448 -1.2 TD (BOTH)Tj /F4 1 Tf 3.2628 0 TD (A)Tj /F6 1 Tf 8.3686 0 0 8.3686 128.4772 438.8072 Tm (1)Tj /F7 1 Tf 11.9552 0 0 11.9552 137.8251 440.6005 Tm (AND)Tj /F4 1 Tf 2.575 0 TD (B)Tj /F6 1 Tf 8.3686 0 0 8.3686 177.6777 438.8072 Tm (4)Tj /F2 1 Tf 11.9552 0 0 11.9552 187.0266 440.6005 Tm [(o)-27.8(ccur,)-333.4(either)-333.3(together)-333.4(or)-333.3(in)-333.3(sequence.)]TJ -6.9102 -1.2 TD [(By)-333.3(applying)-333.4(the)-333.4(rst)-333.4(rule)-333.3(of)-333.4(probabilit)27.7(y)83.3(,)-333.3(w)27.8(e)-333.4(get)]TJ /F4 1 Tf 1.5991 -1.5222 TD (P)Tj /F2 1 Tf 0.7809 0 TD (\()Tj /F4 1 Tf 0.3888 0 TD (C)Tj /F6 1 Tf 8.3686 0 0 8.3686 146.0613 406.2622 Tm (5)Tj /F2 1 Tf 11.9552 0 0 11.9552 151.4241 408.0555 Tm 0.2778 Tc (\)=)Tj /F4 1 Tf 1.7223 0 TD 0 Tc (P)Tj /F2 1 Tf 0.7809 0 TD (\()Tj /F4 1 Tf 0.3888 0 TD (A)Tj /F6 1 Tf 8.3686 0 0 8.3686 194.9649 406.2622 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 202.9848 408.0555 Tm ()Tj /F4 1 Tf 0.8889 0 TD (B)Tj /F6 1 Tf 8.3686 0 0 8.3686 222.6799 406.2622 Tm (4)Tj /F2 1 Tf 11.9552 0 0 11.9552 228.0428 408.0555 Tm 0.2223 Tc (\)+)Tj /F4 1 Tf 1.6112 0 TD 0 Tc (P)Tj /F2 1 Tf 0.7808 0 TD (\()Tj /F4 1 Tf 0.3889 0 TD (A)Tj /F6 1 Tf 8.3686 0 0 8.3686 270.2555 406.2622 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 278.2755 408.0555 Tm ()Tj /F4 1 Tf 0.8889 0 TD (B)Tj /F6 1 Tf 8.3686 0 0 8.3686 297.9706 406.2622 Tm (3)Tj /F2 1 Tf 11.9552 0 0 11.9552 303.3335 408.0555 Tm 0.2222 Tc (\)+)Tj /F4 1 Tf 1.6111 0 TD 0 Tc (P)Tj /F2 1 Tf 0.7809 0 TD (\()Tj /F4 1 Tf 0.3889 0 TD (A)Tj /F6 1 Tf 8.3686 0 0 8.3686 345.5462 406.2622 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 353.5661 408.0555 Tm ()Tj /F4 1 Tf 0.8889 0 TD (B)Tj /F6 1 Tf 8.3686 0 0 8.3686 373.2613 406.2622 Tm (2)Tj /F2 1 Tf 11.9552 0 0 11.9552 378.6241 408.0555 Tm 0.2222 Tc (\)+)Tj /F4 1 Tf 1.6111 0 TD 0 Tc (P)Tj /F2 1 Tf 0.7809 0 TD (\()Tj /F4 1 Tf 0.3889 0 TD (A)Tj /F6 1 Tf 8.3686 0 0 8.3686 420.8369 406.2622 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 428.8568 408.0555 Tm ()Tj /F4 1 Tf 0.8888 0 TD (B)Tj /F6 1 Tf 8.3686 0 0 8.3686 448.5519 406.2622 Tm (1)Tj /F2 1 Tf 11.9552 0 0 11.9552 453.9148 408.0555 Tm (\))Tj /F3 1 Tf 0.3889 0 TD (})Tj /F4 1 Tf 0.5 0 TD (,)Tj /F2 1 Tf -32.1232 -1.5223 TD [(whic)27.7(h)-258.1(follo)27.8(ws)-258.2(from)-258.2(the)-258.2(fact)-258.1(that,)-273.3(here,)-273.2(w)27.7(e)-258.1(ha)27.8(v)27.8(e)-258.2(a)-258.2(union)-258.2(of)-258.2(m)27.8(utually)-258.2(exclusiv)27.7(e)-258.1(e)0(v)27.7(e)0(n)27.7(ts.)]TJ 0 -1.2 TD (But)Tj /F4 1 Tf 2.0647 0 TD (A)Tj /F5 1 Tf 8.3686 0 0 8.3686 114.1539 373.7173 Tm (i)Tj /F2 1 Tf 11.9552 0 0 11.9552 123.0595 375.5106 Tm (and)Tj /F4 1 Tf 2.023 0 TD (B)Tj /F5 1 Tf 8.3686 0 0 8.3686 156.3128 373.7173 Tm (j)Tj /F2 1 Tf 11.9552 0 0 11.9552 166.2755 375.5106 Tm [(are)-411.9(indep)-27.8(enden)27.7(t)-411.9(e)0(v)27.8(e)0(n)27.7(t)0(s)-411.9(for)-412(all)]TJ /F4 1 Tf 13.6818 0 TD [(i,)-166.7(j)]TJ /F2 1 Tf 1.258 0 TD [(,)-431.6(suc)27.8(h)-411.9(that)-411.9(the)-412(outcome)-412(of)-412(one)]TJ -22.1143 -1.2 TD [(do)-27.8(es)-333.4(not)-333.3(aect)-333.3(the)-333.4(outcome)-333.4(of)-333.4(the)-333.3(other.)-444.5(Therefore,)]TJ /F4 1 Tf 7.2183 -1.9377 TD (P)Tj /F2 1 Tf 0.7809 0 TD (\()Tj /F4 1 Tf 0.3888 0 TD (A)Tj /F5 1 Tf 8.3686 0 0 8.3686 189.7504 336.2059 Tm (i)Tj /F3 1 Tf 11.9552 0 0 11.9552 196.3875 337.9992 Tm ()Tj /F4 1 Tf 0.8889 0 TD (B)Tj /F5 1 Tf 8.3686 0 0 8.3686 216.0827 336.2059 Tm (j)Tj /F2 1 Tf 11.9552 0 0 11.9552 221.1198 337.9992 Tm 0.2778 Tc (\)=)Tj /F4 1 Tf 1.7222 0 TD 0 Tc (P)Tj /F2 1 Tf 0.7808 0 TD (\()Tj /F4 1 Tf 0.3889 0 TD (A)Tj /F5 1 Tf 8.3686 0 0 8.3686 264.6605 336.2059 Tm (i)Tj /F2 1 Tf 11.9552 0 0 11.9552 268.6406 337.9992 Tm (\))Tj /F3 1 Tf 0.6112 0 TD ()Tj /F4 1 Tf 1 0 TD (P)Tj /F2 1 Tf 0.7808 0 TD (\()Tj /F4 1 Tf 0.3889 0 TD (B)Tj /F5 1 Tf 8.3686 0 0 8.3686 310.9549 336.2059 Tm (j)Tj /F2 1 Tf 11.9552 0 0 11.9552 315.992 337.9992 Tm 0.2778 Tc (\)=)Tj 2.0923 0.6765 TD 0 Tc (1)Tj ET 338.01 341.188 11.955 -0.478 re f BT 11.9552 0 0 11.9552 338.0164 329.799 Tm (36)Tj 2.12 0.6859 TD [(for)-333.4(all)]TJ /F4 1 Tf 3.5861 0 TD [(i,)-166.7(j)]TJ /F2 1 Tf 1.2581 0 TD (;)Tj -28.504 -1.8026 TD [(and)-333.3(it)-333.3(follo)27.8(ws)-333.3(that)]TJ /F4 1 Tf 1.6673 -1.7432 TD (P)Tj /F2 1 Tf 0.7809 0 TD (\()Tj /F4 1 Tf 0.3888 0 TD (C)Tj /F6 1 Tf 8.3686 0 0 8.3686 122.9659 293.8159 Tm (5)Tj /F2 1 Tf 11.9552 0 0 11.9552 128.3288 295.6092 Tm 0.2778 Tc (\)=)Tj /F4 1 Tf 1.7222 0 TD 0 Tc (P)Tj /F2 1 Tf 0.7809 0 TD (\()Tj /F4 1 Tf 0.3888 0 TD (A)Tj /F6 1 Tf 8.3686 0 0 8.3686 171.8695 293.8159 Tm (1)Tj /F2 1 Tf 11.9552 0 0 11.9552 177.2334 295.6092 Tm (\))Tj /F4 1 Tf 0.3888 0 TD (P)Tj /F2 1 Tf 0.7809 0 TD (\()Tj /F4 1 Tf 0.3889 0 TD (B)Tj /F6 1 Tf 8.3686 0 0 8.3686 204.9355 293.8159 Tm (4)Tj /F2 1 Tf 11.9552 0 0 11.9552 210.2984 295.6092 Tm 0.2223 Tc (\)+)Tj /F4 1 Tf 1.6112 0 TD 0 Tc (P)Tj /F2 1 Tf 0.7809 0 TD (\()Tj /F4 1 Tf 0.3888 0 TD (A)Tj /F6 1 Tf 8.3686 0 0 8.3686 252.5111 293.8159 Tm (2)Tj /F2 1 Tf 11.9552 0 0 11.9552 257.875 295.6092 Tm (\))Tj /F4 1 Tf 0.3888 0 TD (P)Tj /F2 1 Tf 0.7809 0 TD (\()Tj /F4 1 Tf 0.3889 0 TD (B)Tj /F6 1 Tf 8.3686 0 0 8.3686 285.5771 293.8159 Tm (3)Tj /F2 1 Tf 11.9552 0 0 11.9552 290.94 295.6092 Tm 0.2223 Tc (\)+)Tj /F4 1 Tf 1.6112 0 TD 0 Tc (P)Tj /F2 1 Tf 0.7808 0 TD (\()Tj /F4 1 Tf 0.3889 0 TD (A)Tj /F6 1 Tf 8.3686 0 0 8.3686 333.1526 293.8159 Tm (3)Tj /F2 1 Tf 11.9552 0 0 11.9552 338.5156 295.6092 Tm (\))Tj /F4 1 Tf 0.3889 0 TD (P)Tj /F2 1 Tf 0.7809 0 TD (\()Tj /F4 1 Tf 0.3889 0 TD (B)Tj /F6 1 Tf 8.3686 0 0 8.3686 366.2187 293.8159 Tm (2)Tj /F2 1 Tf 11.9552 0 0 11.9552 371.5815 295.6092 Tm 0.2222 Tc (\)+)Tj /F4 1 Tf 1.6111 0 TD 0 Tc (P)Tj /F2 1 Tf 0.7809 0 TD (\()Tj /F4 1 Tf 0.3889 0 TD (A)Tj /F6 1 Tf 8.3686 0 0 8.3686 413.7943 293.8159 Tm (4)Tj /F2 1 Tf 11.9552 0 0 11.9552 419.1572 295.6092 Tm (\))Tj /F4 1 Tf 0.3889 0 TD (P)Tj /F2 1 Tf 0.7809 0 TD (\()Tj /F4 1 Tf 0.3888 0 TD (B)Tj /F6 1 Tf 8.3686 0 0 8.3686 446.8603 293.8159 Tm (1)Tj /F2 1 Tf 11.9552 0 0 11.9552 452.2231 295.6092 Tm 0.2778 Tc (\)=)Tj 2.0922 0.6765 TD 0 Tc (4)Tj ET 1 i 474.21 298.35 11.955 0.478 re f BT 11.9552 0 0 11.9552 474.2466 287.4079 Tm (36)Tj /F4 1 Tf 1.12 0.686 TD (.)Tj /F2 1 Tf -34.0549 -1.8027 TD [(The)-398.9(principle)-398.9(that)-398.9(has)-398.9(b)-27.8(een)-398.8(in)27.7(v)27.8(o)0(k)27.8(e)0(d)-398.8(i)0(n)-398.9(solving)-398.9(this)-398.9(problem,)-415.3(whic)27.7(h)-398.9(has)-398.9(pro)27.8(vided)]TJ 0 -1.2 TD [(the)-333.4(probabilities)-333.4(of)-333.4(the)-333.4(ev)27.8(en)27.7(ts)]TJ /F4 1 Tf 13.3473 0 TD (A)Tj /F5 1 Tf 8.3686 0 0 8.3686 249.0391 257.9185 Tm (i)Tj /F3 1 Tf 11.9552 0 0 11.9552 255.6762 259.7118 Tm ()Tj /F4 1 Tf 0.8888 0 TD (B)Tj /F5 1 Tf 8.3686 0 0 8.3686 275.3704 257.9185 Tm (j)Tj /F2 1 Tf 11.9552 0 0 11.9552 280.4085 259.7118 Tm [(,)-333.3(i)0(s)-333.4(the)-333.3(follo)27.8(wing:)]TJ /F7 1 Tf -14.7212 -1.6049 TD [(The)-527.3(pr)51.1(ob)51.2(ability)-527.3(of)-527.3(the)-527.2(joint)-527.3(o)51.1(c)51.2(curr)51.1(enc)51.1(e)-527.3(o)0(f)-527.2(two)-527.2(statistic)51.1(al)-51.2(ly)-527.2(indep)51.1(endent)]TJ 0 -1.2 TD [(events)-326.7(is)-326.7(the)-326.8(pr)51.1(o)51.1(duct)-326.7(of)-326.7(their)-326.7(individual)-326.8(or)-326.7(mar)51.1(ginal)-326.7(pr)51.1(ob)51.1(abilities.)-449.6(Thus,)-333(if)]TJ /F4 1 Tf T* (A)Tj /F7 1 Tf 1.1078 0 TD (and)Tj /F4 1 Tf 1.9422 0 TD (B)Tj /F7 1 Tf 1.1664 0 TD [(ar)51.1(e)-357.8(statistic)51.1(al)-51.2(ly)-357.7(indep)51.1(endent,)-357.8(then)]TJ /F4 1 Tf 15.0393 0 TD (P)Tj /F2 1 Tf 0.7809 0 TD (\()Tj /F4 1 Tf 0.3889 0 TD (A)Tj /F3 1 Tf 0.9722 0 TD ()Tj /F4 1 Tf 0.8889 0 TD (B)Tj /F2 1 Tf 0.8087 0 TD 0.2778 Tc (\)=)Tj /F4 1 Tf 1.7222 0 TD 0 Tc (P)Tj /F2 1 Tf 0.7808 0 TD (\()Tj /F4 1 Tf 0.3889 0 TD (A)Tj /F2 1 Tf 0.75 0 TD (\))Tj /F3 1 Tf 0.6111 0 TD ()Tj /F4 1 Tf 1 0 TD (P)Tj /F2 1 Tf 0.7809 0 TD (\()Tj /F4 1 Tf 0.3889 0 TD (B)Tj /F2 1 Tf 0.8087 0 TD (\))Tj /F7 1 Tf 0.3889 0 TD (.)Tj /F1 1 Tf -32.7158 -1.605 TD [(Conditional)-491.9(probabilities.)]TJ /F2 1 Tf 13.6303 0 TD [(No)27.7(w)-427.6(let)-427.7(us)-427.7(dene)-427.6(a)-427.7(fourth)-427.6(set)-427.7(of)-427.7(ev)27.8(en)27.7(ts)]TJ /F3 1 Tf 18.3404 0 TD ({)Tj /F4 1 Tf 0.5 0 TD (D)Tj /F5 1 Tf 8.3686 0 0 8.3686 478.5953 190.851 Tm (k)Tj /F2 1 Tf 11.9552 0 0 11.9552 484.4782 192.6442 Tm (;)Tj /F4 1 Tf 0.4444 0 TD (k)Tj /F2 1 Tf 0.987 0 TD (=)Tj -35.2222 -1.2 TD (2)Tj /F4 1 Tf 0.5 0 TD (,)Tj /F2 1 Tf 0.4444 0 TD (3)Tj /F4 1 Tf 0.5 0 TD 0.1666 Tc (,...,)Tj /F2 1 Tf 2.2222 0 TD 0 Tc (12)Tj /F3 1 Tf 1 0 TD (})Tj /F2 1 Tf 0.9263 0 TD [(corresp)-27.8(onding)-426.3(to)-426.4(the)-426.4(v)55.5(alues)-426.4(of)]TJ /F4 1 Tf 13.954 0 TD (x)Tj /F2 1 Tf 0.8558 0 TD (+)Tj /F4 1 Tf 1.062 0 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