## Related questions with answers

A tablet computer transmits a file over a wi-fi link to an access point. Depending on the size of the file, it is transmitted as N packets where N has PMF

$P_{N}(n)=\left\{\begin{array}{ll}{c / n} & {n=1,2,3,} \\ {0} & {\mathrm { otherwise. }}\end{array}\right.$

(a) Find the constant c. (b) What is the probability that N is odd? (c) Each packet is received correctly with probability p, and the file is received correctly if all N packets are received correctly if all N packets are received correctly. Find P[C], the probability that the file is received correctly.

Solution

Verified#### (a)

The range of $N$ is equal to $S_N = \{1, 2, 3\}$. The constant $c$ is obtained from the equation $1 = \sum_n P_N(n)$. Therefore, we have that

$\begin{align*} 1 = \sum_{n \in S_N} P_N(n) = c + \frac{c}{2} + \frac{c}{3} = \frac{11}{6}c \Rightarrow c= \frac{6}{11}. \end{align*}$

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