There are two competing designs for a certain semiconductor circuit. The lifetime of the first (in hours) is exponentially distributed with λ = 10⁻⁴, and the lifetime of the second is lognormally distributed with μ = 6 and σ² = 5.4.

a. Use a simulated sample of size 1000 to estimate the probability that a circuit with the first design lasts longer than one with the second design. 

b. Estimate the probability that a circuit with the first design lasts more than twice as long as one with the second design.