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 by
p(x)={ cx for x=1,2,3,4, or 5
{ 0 otherwise
where c is a constant.
Find P(X = 2).

Answer 1

Explanation:

given that 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 by

p(x)={ cx for x=1,2,3,4, or 5

{ 0 otherwise

where c is a constant.

Let us write pdf as follows

x 1 2 3 4 5 Total

p c 2c 3c 4c 5c 15c

Since total probability = 1

we get

`c=(1)/(15)`

P(X=2)=2c =
`(2)/(15)`