# Rockets are launched until the first successful launching has taken place.if this does not occur within 5 atte?

Rockets are launched until the first successful launching

has taken place.if this does not occur within 5 attempts,the

experiment is halted and the equipment inspected.suppose that

there is a constant probability of 0.8 of having a successful

launching and that successive attempts are independent.Assume

that the cost of the first launching is K dollars while subsequent

launching cost K/3 dollars.whenever a successful launching take place,a certain amount of information

is obtained which may be expressed as financial gain of,say 'C' dollars.if 'T' is the net cost of this

experiment,find the probability distribution of T?

### 1 Answer

- 6 years agoFavorite Answer
T = K + C, (K is a negative number).

T can have 6 different values, K, K+K/3+C, K+2*(K/3+C), K+3*(K/3+C), K+4*(K/3+C), K+4*K/3+5*C, which corresponds to 0,1, 2,3 and 4 attempts before succeeding and 5 unsuccessful attempts.

P(T=K) = 0.8

P(T = K+K/3+C ) = 0.2*0.8

P(T = K+2*(K/3+C) ) = 0.2^2*0.8

P(T = K+3*(K/3+C) ) = 0.2^3*0.8

P(T = K+4*(K/3+C) ) = 0.2^4*0.8

P(T = K+4*K/3+5*C)= 0.2^5