04 of the actual probability with probability 095

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: : 1. . Suppose that we have graduates and get i.i.d. random variables 1 when the ith graduate attends the graduating ceremony, 0 when the We define ith graduate doesn’t attend the graduating ceremony. 1 and 0 1 . (1’) ∑ Denote the estimate as 0.04, . . (2’) From the Chebyshev inequality: | | 1 Solve the inequality, we get that 1 0.95 (1’) 3125. (1’) 4. (Lec. 21, 5 points) Packet transmission time on a certain Internet link is independent and identically distributed according to a geometric distribution with mean 3 ms. Suppose 800 packets are transmitted. Use the central limit theorem to estimate the required transmission time so that all the packets can be transmitted with probability 99%. (Hint: the Q-function table can be found on slides 27 in Lec. 11). Solution: Denote the transmission time for the ith packet is ms, 1. . , 800. 3, we get that For geometric variable: and 6. (1’) ∑ The total transmission time: ms According to the central limit theorem, approaches a Gaussian distribution with mean 2400 and variance 4800. (2’) Let denote the required transmission time, to satisfy the requirement: 1 0.99 (1’) √ After solving the inequality above, we get that 2561ms. (1’) 5. (Lec. 23, 5 points) We flip a fair coin and define a random process sin if the head shows, and 2 if the tail shows. (a) Find . (2 points) for 1. (3 points) (b) Find Solution: The random process can be expressed as sin 2, sin (a) (b) | (2’) 0, ,0 1, 0 2 (3) 2 , if head shows; if tail shows. as follows:...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online