Answer:
1. 0.108368
2. 0.188876
Step-by-step explanation:
Let X be the exponential random variable that represents the lifetime of a computer.
i.e. [tex]X\sim Exp(0.001)[/tex]
The probability that the computer will function more than 2000 days can be computed as follows:
P(X > 2000)
: [tex]f_X(x) = \lambda e^{-\lambda x[/tex]
P(X > 2000) = 1 - P(X< 2000)
P(X > 2000) = exp(-2000/β) = e⁻²²
P(X > 2000) = 0.108368
2.
By applying conditional probability;
[tex]P(X>2000 \bigg | X>500) =\dfrac{P(X>2000 \ \cap \ X>500)}{P(X> 500)}[/tex]
[tex]P(X>2000 \bigg | X>500) =\dfrac{P(X>2000 )}{P(X> 500)}[/tex]
[tex]P(X>2000 \bigg | X>500) =\dfrac{0.108368 }{0.57375}[/tex]
[tex]\mathbf{P(X>2000 \bigg | X>500) =0.188876}[/tex]
