We model the life span of a chip (in years) with a distribution that has the...

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We model the life span of a chip (in years) with a distribution that has the following cumulative distribution function (cdf). F(x) = { 0 x ≤ 0 1- exp(-x) x>0 with a>0 and ß> 0 being parameters. a) (1 point): Determine the probability density function (pdf) of the distribution. b) (1.5 points): Suppose a = 2 and B 1. What is the probability that the chip works longer than four years? What is the probability that the chip stops working in the time interval [5; 10] years? c) (1.5 points): How large is the median of a life span (for general a, ß)? We model the life span of a chip (in years) with a distribution that has the following cumulative distribution function (cdf). F(x) = { 0 x ≤ 0 1- exp(-x) x>0 with a>0 and ß> 0 being parameters. a) (1 point): Determine the probability density function (pdf) of the distribution. b) (1.5 points): Suppose a = 2 and B 1. What is the probability that the chip works longer than four years? What is the probability that the chip stops working in the time interval [5; 10] years? c) (1.5 points): How large is the median of a life span (for general a, ß)?