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

Answer:

Step-by-step 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

$c=\frac{1}{15}$

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