Hi, need to submit a 750 words essay on the topic Quantitative Techniques for Business.Download file to see previous pages... The probability is less than the normal distribution and it is wider at th

Hi, need to submit a 750 words essay on the topic Quantitative Techniques for Business.

The probability is less than the normal distribution and it is wider at the mean. 4. Under the assumption that the returns of each asset are drawn from an independently and identically distributed normal distribution, are the expected returns statistically different from zero for each asset? State clearly the null and alternative hypothesis in each case. 5. Assume the returns from each asset are independent from each other, are the mean returns statistically different from each other? 6. Calculate the correlation matrix of the returns. 7. Is the assumption of independence realistic? If not, re-test the hypotheses in Question 5 using appropriate test statistics. Compare the results to the results obtained in Question 5. 8. If you can only choose maximum of two assets into a portfolio, which will you choose? What are the optimal weights and the optimal expected returns? State clearly your objective function and provide step-by-step derivations.I would choose AUD per YEN and AUD per UKP since they have higher total returns than the rest. The objective function is to take the portfolio with the highest positive return, as it will maximize profit. 9. Bonus question: Why is it not realistic to assume these rates follow a normal distribution? Moreover, is Treasury bill safer than the other three exchange rates? The rates do not follow a normal distribution since they are not independent of each other. Treasury bill is safer than the other exchange rates since it has a positive return to itself and no negative returns from, the others.