Question

A computer sends a packet of information along a channel and waits for a return signal acknowledging that the packet has been received. If no acknowledgment is received within a certain time, the packet is re-sent. Let X represent the number of times the packet is sent. Assume that the probability mass function of X is given byp(x) ={ cx , for x=0,1,2,...50 , otherwieFind P(X = 2).

Answer 1

Answer:

The answer is "$\frac{2}{15}$" .

Explanation:

$\to x = 0, 1, 2, 3, 4, 5\\\\\to p(x) \ for \ x \ = 0, 1, 2, 3, 4, 5 = 0\\\\ \to c, 2c, 3c , 4c, 5c = 1\\\\\to 0 + c + 2c + 3c + 4c + 5c = 1\\\\\to 15c = 1\\\\\to c = \frac{1}{15}$

$\to p(x) \ for \ x \ = 0, 1, 2, 3, 4, 5 = 0\\\\ \to \frac{1}{15}, \frac{2}{15}, \frac{3}{15}, \frac{4}{15}, \frac{5}{15}$  

$\to P(X=2)=\frac{2}{15}$