Question: =+contain exactly j observations from the X sample, j 0; 1; ... ; m. a Verify that S0 S1 Sm

=+contain exactly j observations from the X sample, j ¼ 0; 1; ... ; m.

ðaÞ Verify that S0 þ S1 þ þ Sm ¼ n þ 1 and S1 þ 2S2 þ þ mSm ¼ m.

ðbÞ If FX ¼ FY, show that the joint distribution of S0; S1; ... ;Sm is given by

ðn þ 1Þ!

s0!s1! sm!

m þ n n

1

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