Suppose that you are given the distribution functions of two…

Suppose that you are given the distribution functions of two random variables X and Y. If Cov(X,Y)=0, are X and Y independent? Answer True/False below and provide a supporting reason on your scratch paper. An answer without a reason will receive 0. If this is not sufficient to determine whether they are independent, choose False and explain why.

A venture capital firm evaluates thousands of startup compan…

A venture capital firm evaluates thousands of startup companies each year. Historically, only 1 out of every 1,000 startups turns out to be successful. The firm uses an initial evaluation test to assess potential. The evaluation test is imperfect: If a startup will be successful, the test returns a positive evaluation with probability 0.8 If a startup will not be successful, the test returns a positive evaluation with 0.05 Show your work on the scratch paper answering Q4-Q6.