12. Guassian distribution: An athlete training for 100 meters race every day can be modeled as a Guassian distribution with a mean of 12 seconds and a variance of 1.5 seconds. Derive the probability density function of him clocking 10.8 seconds and 12.4 seconds. Write the equation to calculate clearly and show the calculation. (2 points) Poisson distribution: Computer screen of a computer system running Microsoft operating system freezes on an average 7 times per 200 hours of operation. What is the probability that it would freeze 9 times in next 200 hours of operation. (1 point) Binomial distribution: Every Two in 100 computers bought from a company need to be replaced. Calculate the mean and variance of the distribution if a lot of 1000 computers is randomly selected. (1 point)