A company is inyestigating the nancial feasibility of asteroid mining. They are only interested in asteroids. greater than 10m in diameter. A statistician proposes that the cumulatiye distribution function for the diameter of asteroids. x, in their range of interest is giyen by: _ 1i] 3 Calculate the associated probability density function, fix}. and then answer the following question: What is the value of the probability density function when x=13? Enter your answer as a decimal 1value accurate to THREE decimal places, rounding as appropriate. The most lucrative type of asteroid to mine are "M-type" {metallic type} asteroids but these are relatively rare, with only 10% of asteroids being M-type. An engineer has developed a test to determine if an asteroid is an M-type and we wish to evaluate the effectiveness of this test. If an asteroid is an M-type asteroid then the test correctly identies it as such 534% of the time. If an asteroid is NOT an M-type then the test in correctly identies it as an Mtype ?% of the time. Draw a labelled frequency tree for the above scenario, working with 1000 asteroids and then answer the following question. 1What is the probability that an asteroid identied as M-type is in fact NOT an Mtype? Enter your answer as a decimal value to TWO decimal places, rounding if needed. e.g. a probability of I in 8 fie. 12.5%} has the decimal value 0.125 which would be rounded to 20F and entered as 0.1 3