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Question: A coin which lands heads with probability p is tossed repeatedly. Assuming independence of the tosses, find formula for
a) P(exactly 5 heads appear in the first 9 tosses):
b) P(the first head appears on the 7th toss)
c) P(the fifth head appears on the 12th toss):
d) P(the same number of heads appear in the first 8 tosses as in the next 5 losses).
A function g(x) is convex if the chord connecting any two points on the function's graph lies above the graph. When g(x) is differentiable, an equivalent condition is that for every x, the tangent line at x lies entirely on or below the graph.
Show that R2 is not a countable union of ranges of a C 1 curves. Hint: Show that the range of a C 1 curve on a finite interval is nowhere dense.
Law school courses often have assigned seating to facilitate the Socratic method. Suppose that there are 100 first-year law students, and each takes the same.
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