Answer:
a) 0.6
b) 15 years
Step-by-step explanation:
a) Since the two blocks have the same probability function, the exponential probability that one of the blocks will fail, is given as
P(X>x) = 1 - e^(-λ.x)
λ = rate parameter = (1/10) = 0.1
x = variable whose probability is required = 10 years.
λ.x = 0.1 × 10 = 1
P(X>10) = (1 - e⁻¹) = 0.632
Probability that both blocks fail = 0.632 × 0.632 = 0.3999
Probability that the satellite will work for more than 10 years = Probability that at least one of the blocks is working = 1 - (probability that both blocks are not working) = 1 - 0.3999 = 0.60
b) Expected lifetime of the satellite for the two blocks in a sort of parallel combination will be given as
E(X) = (1/λ) + (1/λ) - [1/(λ + λ)]
E(X) = 10 + 10 - 5 = 15 years
Hope this Helps!!!
