Kindly answer the following questions.

Question 1.19 In a claims department of a motor insurance company, a sample of 12 claims had a mean of 1845 and a standard deviation of $208. It was then discovered that two mistakes were made; a claim of $526 was classified wrongly and is removed from the set of 12 claims, and a new claim of $1,034 is added to make the sample back up to 12. Calculate the sample mean and standard deviation of the modified sample of 12 claims. [4] Question 1.20 An actuarial recruitment company places adverts in three publications with probabilities of 0.2, 0.3 and 0.5 respectively. The probability that the recruitment company gets an enquiry from an advert in the first publication is 0.001. The probabilities for the other two publications are 0.002 and 0.004 respectively. Given that the company has just received an enquiry, calculate the probability that it came from an advert in the first publication. [3]Question 1.21 A continuous random variable Y' has PDF: (y(y-1)()-2)+0.4 0Sys2 f ( y) = 2