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?
- 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