hw3_sol - ECE 139 Part A: Probability and Statistics HW#3 -...

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ECE 139 Probability and Statistics HW#3 - Solutions Part A: ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 1.6.3 P[A] = 1/4, P[B] = 1/8, P[C] = 5/8, P[D] = 3/8, A & B are disjoint. C& D are independent. (a) A & B are disjoint. A B = P[A B] = 0 (i.e. A is a subset of B c .) P[A B] = P[A] + P[B] = 3/8 P[A B c ] = P[A] = 1/4 P[A B c ] = P[B c ] = 1 – P[B] = 1 – 1/8 = 7/8 (b) P[A]×P[B] = 1/4 × 1/8 = 1/32 ≠ 0 = P[A B] (c) C & D are independent. P[C D] = P[C]×P[D] = 5/8 × 3/8 = 15/64 P[C D c ] = P[C] - P[C D] = 5/8 – 15/64 = 25/64 → P[C c D c ] = P[(C D) c ] = 1 – P[C D] = 1 – (P[C] + P[D] – P[C D]) = 1 – 5/8 – 3/8 + 15/64
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This note was uploaded on 08/08/2010 for the course ECE PROF. VOLK taught by Professor Volkanrodoplu during the Summer '10 term at UCSB.

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hw3_sol - ECE 139 Part A: Probability and Statistics HW#3 -...

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