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You are designing a packet voice transmission system. A speech signal is segmented into 10 ms chunks, and sent in packets. However; to save bandwidth/ the signal is only packetized when the
Speaker is NOT silent. If you have a group of N speakers in diﬁerent conversations, chances are not all of them will be
speaking at once. You design your system to handle up to 8 simultaneous speakers. HOW many calls can you admit
into your system, and ensure that you exceed capacity no more than 1% of the time? , i / {ﬁt/£64”?
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of the race is 0.2. Cars break down independently of each other. (a) What is the probability that exactly two cars ﬁnish the race?
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_ A A e ECE 302: Probabilistic Methods in Electrical and Computer Engineering Fall 29w: 2:» r '7 PURDUE Instructor: Prof. A. R. Reibman U N I V L R S I T Y In—class problems Fall 33:6 219W ‘
(August 3% %) ’lwo ab 69 L4 262917 6 gf‘dég‘ [WEEKS SPrECl'G‘ed) we die Exercise 1 . Roll 2 dice and observe the pair of the number on the ﬁrst die and the number on the second die.
Let A1 2 {doubles} and A2 : {the sum of the two numbers is 6}.
Sketch the sample space, and A1 and A2. How many outcomes are in A1 U A2? 5 : gm») 5 #79346] j Mvﬁl/Cl' A 2, 2/ j'é, 71— A5? (Will/'1), (3,3), 
Wilt/)Jéﬁjﬂé/(O; Exercise 4. (FROM HOMEWORK DUE FRIDAY)
For each of the following relations, determine which is valid for arbitrary events A, B, and 0. (Note: to be true “for arbitrary events”, it must be true for any such event. Use a Venn diagram if it is
helpful.) (On the exam, this was a True / False question. For this homework, show whether it is true or false.)
(AUBVUC)C=IACUBCUCC (AﬂB) U(AﬂBC) U (ACﬂB) = (ACDBC)C (A—B)—C::A—(B—C’). ( AUB)ﬂ(ACLJBC)=(AnBC)LJ(AcﬂB)LJ(ACﬂBﬂOC) ...
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