| Line 1: | Line 1: | ||
| − | <nowiki> | + | <nowiki> |
| − | + | ||
From the memoryless property of Exponential Distribution function: | From the memoryless property of Exponential Distribution function: | ||
| + | |||
Suppose E1,λ and E1,μ are independent, then; | Suppose E1,λ and E1,μ are independent, then; | ||
| − | P[min{ E1,λ , E1,μ } > t] = P[E1,λ > t] . P[E1,μ } > t] | + | |
| − | + | P [min{ E1,λ , E1,μ } > t] = P [E1,λ > t] . P [E1,μ } > t] | |
| − | + | = eˉλt . eˉμt | |
| + | = eˉ(λ + μ)t | ||
| + | |||
which shows that minimum of E1,λ and E1,μ is exponentially distributed. | which shows that minimum of E1,λ and E1,μ is exponentially distributed. | ||
| + | |||
So, | So, | ||
| + | |||
E1, λ1+ λ2+ λ3+……. λn = min { E1,λ1, E1,λ2, E1,λ3, ……….., E1,λn } | E1, λ1+ λ2+ λ3+……. λn = min { E1,λ1, E1,λ2, E1,λ3, ……….., E1,λn } | ||
| + | |||
Here, if we put λ = 1, then; | Here, if we put λ = 1, then; | ||
| + | |||
E1, 1+ 2+ 3+……. n = min { E1,1, E1,2, E1,3, ……….., E1,n } | E1, 1+ 2+ 3+……. n = min { E1,1, E1,2, E1,3, ……….., E1,n } | ||
| + | |||
| + | </nowiki> | ||
Revision as of 18:49, 6 October 2008
From the memoryless property of Exponential Distribution function: Suppose E1,λ and E1,μ are independent, then; P [min{ E1,λ , E1,μ } > t] = P [E1,λ > t] . P [E1,μ } > t] = eˉλt . eˉμt = eˉ(λ + μ)t which shows that minimum of E1,λ and E1,μ is exponentially distributed. So, E1, λ1+ λ2+ λ3+……. λn = min { E1,λ1, E1,λ2, E1,λ3, ……….., E1,λn } Here, if we put λ = 1, then; E1, 1+ 2+ 3+……. n = min { E1,1, E1,2, E1,3, ……….., E1,n }
