A variation on a familiar theme: A packet is received correctly by an end user with probability p. To increase the likelihood that an important message is received, the packet is sent repeatedly N times. Let random variable X be the number of copies received correctly by the end user. a) Find the PMF PX(x). b) If p = 0.9, how large should N be to ensure that with probability 0.99 at least one copy of the message is received

a) X can take the values {0,1,2,3,...,n}

The probability mass function of x is defined for k copies received correctly as:

b) N should be N=2 to ensure that with probability 0.99 at least one copy of the message is received.

Step-by-step explanation:

The variable X:number of copies received correctly by the end user can be modeled as a binomial variable, as it is a sum of n Bernoulli variables with probability p.

X can take the values {0,1,2,3,...,n}

The probability mass function of x is defined for k copies received correctly as:

being p: the probability that a packet is received correctly by an end user, and q=1-p: the probability that a packet is not received correctly by an end user.

b) We have to calculate n so as to have a probability P(x≥1)=0.99, when p=0.9.

yes

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