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

where c is a constant.

a. Find the value of the constant c so that p(x) is a probability mass function.

b. Find P(X = 2).

c. Find the mean number of times the packet is sent.

d. Find the variance of the number of times the packet is sent.

e. Find the standard deviation of the number of times the packet is sent.

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for x = 1, 2, 3, 4, or 5 otherwise p(x) = сх