Provide step by step solution to the following questions. Kindly ensure precision.

For class surveying different economic systems, I read a book on Marxism and its core beliefs. As I read, I came to learn that the Marxist view of economics depends heavily on the Labor Theory of Value since Marx believed that the value of a good was determined by the amount of labor.

But, from what I understand, the economic community no longer accepts the Labor Theory of Value due to its inability to explain the Diamond-Water Paradox.

How is it then, that certain economists still adhere to the Marxist view of economics? How do they have Marxism explain the Diamond-Water Paradox?

Claims under a certain type of insurance policy occur as a Poisson process so that the number of claims arising from a policy in one calendar year is a Poisson random variable with mean / . In order to estimate / a random sample of a such policies is examined and it is found that no of these policies incurred no claims during the last full calendar year, m of them incurred one claim and the remainder incurred more than one claim. (i) Write down the likelihood of these observations and show that the maximum likelihood estimator / is a solution of the equation: m - (no +n ) ate" (np + non-m)=0 [ You do not need to verify that a maximum is attained.] [10] (ii) A random sample of 20 such policies yields no =8 and n =7. By using the tables of the cumulative Poisson distribution, or otherwise, to find a good starting approximation for / and then using trial and error (or a more sophisticated method), determine // correct to two decimal places. [7] [Total 17]A payment stream, where the payment at time ? is 1+0.3r, is received continuously between times 7 and 9. Calculate the present value of this payment stream at time 5 if the force of interest at time / is given by: 0.002 + 0.01/ +0.0004/ 051