Question: 1.* 2. Let {X), j ~ I} be a sequence of independent r. v.' s having the Bemoullian d.f. POI + (1 -P )00,0 <

1.* 2. Let {X), j ~ I} be a sequence of independent r. v.' s having the Bemoullian d.f. POI + (1 -P )00,0 < P < 1. An r-run of successes in the sample sequence {X)(w), j ~ I} is defined to be a sequence of r consecutive

"ones" preceded and followed by "zeros". Let N n be the number of r-runs in the first n terms of the sample sequence. Prove a central limit theorem for N n'

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