Answer: the number of devices expected to fail during the second month is 24
Step-by-step explanation:
Given that
The device has a constant failure rate with MTTF of 2 months.
As the device has constant failure rate so it has exponential failure distribution
f(t) = λe^-λt
Here MTTF = 1/ λ
so λ = 1/2 Months⁻¹ = 0.5 Months⁻¹ and from the question, Number of devices = 100
E( 1 < x < 2) = E ( x < 2) - E (x < 1)
so E(x < X) can be calculated with λ = 0.5 Months⁻¹ will be calculated as the failure function
f(x) = λ exp ( - λ×t) for t > 0
F (x>0) = 1 - exp( - λx)
so E ( 1 < x < 2) = E ( x < 2) - E (x < 1)
E ( x < 2) = 1 - exp(-0.5 × 2) = 0.6321 ; E (x<1) = 1 - exp(-0.5 × 2) = 1 - exp( -0.5) = 0.3934
so E ( 1 < x < 2) = 0.6321 - 0.3934 = 0.2387
so the number of devices expected to fail during the second month is;
100 × 0.2387 = 23.87 ≈ 24
