Question

Problem 2 (25 Points) Monitor comestive phone call going through a tation on the intersection of Delt-line Road and Preston Roul Clay chall un either a voice call (if is speaking or a data call of the call is c rying non-voice signal). Note that C- 1 if call. voice, otherwise -0. Voice and data callo arrive with probability p and I-P, respectively. Now consider a random Variable Nowhere N G + ... + is the number of voice calles in a cutive plone calls 1. (poanda) What kind of random variable ? 2. painda) Please provide the range of random variable Ng 3. ( paint) Find the PMF of random variable for p 0 .6 4. (5 points) Find the ODF of randow variable for p =0.6. 5. (5 pounds) Voice calle cont 25 cente each and data calle 50 cento each. Torm 7 denotes the cost of the telephone calls monitored at the han station Find the PMF of random Variable Ts for p=0.6. 6. (5 points) Find the PMF of NA

Answer 1

I hit ci be the Classifies ith station as a such that - Ci= random variable phone call through voice call or a that the base data coll. 0 if call is ith call i a i a data voice call call Given - P(i=0) = Pra = 1) 1-b. Then the random varlable Ci is a Ben Bernoulli variate that takes only two values, ok 1 with probabilities (-p) t p respectively & Given. Nn = G + C + - + Cn Ng = Got Cz + is the sum of 3 Bernoulli variates that are independeur each other we Then, the range of Nz - SNg = 0, 1,2,3. Sum results PMF of independent in Binomial of Nan for Bernoulli variates distribution. Therefore, probability of sucdess Р ама те, 1-р for n=3, p = 0.6, P (N3 = 2) = 3 Cx (0.6) * (0.4) 3-2

Date Page CDF of a random variable N3, which follows a Binomial distribution with parameter, n = 3, p=0.6 , will be I given by a P[Ng <) C2 (0.6770.439