Question

E. A coin with probabiltiy p of heads is tossed till the first head occurs. It 1S is then tossed again till the first tail occurs. Let X be the total number of tosses required (a) Find the PMF of X, (b) Find the mean and variance of X

Answer 1

XTota) no of oses hen poc6ble values oP x 01,2, The prob of qetng head on PCI-b pmfo given by n 1,2 To find expectafon or mean nel 古. jn this case Prob.of qettina bead i V2 That means 4herS GOゾchan,-10 genina-bead;

To find vr fance rs we broo the mean of X 2 C Takeトcomin) on R fdbOu)side the braoket -be 2. tt+ t+ Mul ipling both thre Sides by t CI- L)2 C1- t3 CI-

2 ト2 ト2 - 2 var (x) 2 =