Each tirne a rnodern trar1srnits one bit, t he receivir1g

Each tirne a rnodern trar1srnits one bit, t he receivir1g rr1oderr1 anal}rzes t he signal that arrives and decides \vhet11er the transmitt ed bit is 0 or 1. It rr1akes an error vvith probability p, independent of whet11er an}' ot11er bit is received correctly. (a) If t he transmission continues until t11e receiving rr1odem rnakes its first error, what is the P JVIF of X , the nl1rr1ber of bits transrr1itted? (b) If IJ = 0.1 , what is t he probability t11at X = 10? \Vhat is the probability t hat x > 10? ( c) If t he rnoderr1 transmits 100 bits, what is the PMF of Y , t he nl1mber of errors? ( d ) If [ J = 0.01 and t he rnoderr1trar1srnits 100 bits, what is t he probability of Y = 2 errors at the recei\rer ? \Vhat is t he probability that y < 2? ( e) If the transmission contir1ues until t he recei\ring modem rr1akes t hree errors, '\vhat is the P JVIF of Z , t 11e nurnber of bits trar1srnitt ed? ( f) If '[J = 0.25, vvhat is t11e probabilit}' of Z = 12 bits transmitted t1ntil the moderr1rnakes three errors?