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2. A hedge fund requires a minimum initial investment of $100,000. Let K be the amount of a money invested in the hedge fund, in thousands of dollars. Let x} = i and 5x = [10|,ooj.Assun1e X is a continuous variable. [a] For what value of c is x} a valid density? (b) What is the average amount of money invested in the hedge fund? {Recall that K is in thousands of dollars]. {(2) What is the probability that an initial investment is exactly $2M,000? [d] What is the probability that an initial investment is between $50,000 and $200,000