Math Question 7: Given the following information on the returns for stock 1 and 2Scenario Probability Return K1 Return K2ω1 0.4 -10%20%ω20.2 0%20%ω3 0.4 20% 10%(a) Find the weights in a portfolio, V, with expected return µV = 46%(b) Compute the risk σV of this portfolio.Answer each part of the question above on paper. Once completed, select “True” below.

Math Question 6: Consider a non-dividend-paying stock whose current price is $100. A market maker writes a one-year call option on this stock and sells it for $4.00. He then proceeds to delta-hedge his commitment by trading in the shares of the underlying stock. The call option’s delta is 0.75, its gamma is 0.08 and its theta is−0.02 per day. The continuously compounded, risk-free interest rate is 4%. The stock price has risen to $101 after one day. Use the delta-gamma-theta approximation to find the change in market maker’s portfolio after one day.Enter your answer in cents (NOT dollars) rounded to two decimal places.

Math Question 2: Assume Black-Scholes framework. Given a non-dividend stock with current price $70 and volatility 30% per annum. The continuously compounded risk free rate is 8% per annum. Consider a European call option with expiry time 1 year and strike price $75. What is the price of a knock-out call with a barrier of $74 (in dollars)?

Math Question 8: Consider three risky securities with expected returns µ1 = 0.08, µ2 = 0.10, µ3 = 0.16 and with the covariance matrix and its inverse given by Screenshot 2025-05-05 at 1.24.45 PM.png (a) Find the weights of the minimum variance portfolio with these three securities. (b) Does this portfolio involve short-selling? Answer each part of the question above on paper. Once completed, select “True” below.

Place the levels of measurement in order from least to most information. Hint: Remember, only the highest two levels involve numbers you can do meaningful math with.

Question: The stem-and-leaf plot below shows the ages of patients seen during one day in a clinic. Stem | Leaf 2 | 3 4 5 8 3 | 0 1 1 2 4 | 2 4 6 9 5 | 1 3 How many patients are 30 years old or older?  

Steles are:

Children’s physical development

Affective development with social understanding may offer children opportunities to 

An integrated curriculum plan in an early care and learning program