ma316hw1 - MA 316 MATHEMATICAL PROBABILITY ASSIGNMENT#1...

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MA 316: MATHEMATICAL PROBABILITY ASSIGNMENT #1 SOLUTIONS: SECTIONS 1.2 AND 1.3 FALL 2003 1.2: For part a), the answer is { x : 0 < x < 5 8 } and for part b), the answer is { ( x, y, z ) : x 2 + y 2 + z 2 < 1 } . For part c), the complement should consist of four pieces that lie outside of the rotated square | x | + | y | ≤ 2 yet inside the open circle x 2 + y 2 < 2. 1.4: In each part a)-d) the two sets are equivalent. 1.5: One example of a nondecreasing sequence of sets is A k = { x : 0 x 1 - 1 /k } . 1.7: For part a), we have lim k →∞ A k = { x | 0 < x < 3 } . Notice that neither the number x = 0 nor the number x = 3 is in this set since neither is any of the sets A k . 1.15: If N ( C ) denotes the number of member of the club and N ( S ) and N ( M ) denote the number of statisticians and mathematicians respectively then using Venn Diagrams one can see that 25 = N ( C ) = N ( S )+ N ( M ) - N ( S M ) = 19+16 - N ( S M ) from which it follows that N ( S M ) = 10. 1.17: Notice that
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This note was uploaded on 09/10/2009 for the course STATS 517 taught by Professor Song during the Fall '07 term at Purdue.

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ma316hw1 - MA 316 MATHEMATICAL PROBABILITY ASSIGNMENT#1...

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