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- a- Find the radius r₁ of the electron in the ground state orbit of doubly ionized potassium which has an atomic number Z = 19.NewThe half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 125 grams of a radioactive isotope, how much will be left after 3 half-lives? Round your answer to the nearest gram.
- Assume that you have obtained the following information for Asset A: Rate of Return Probability 5.5% 25% 7.25% 55% 11% 20% Compute the expected rate of return for Asset A, using the information provided in thechart above Assume that the standard deviation of the expected returns for Asset A is 1.87%. With information and the expected rate of return that you calculated for Asset A in Part A of this problem, compute the co-efficient of variation for Asset A.The following table gives the monthly inflow and contemplated demand from a proposed reservoir. Estimate the minimum storage that is necessary to meet the demand. If the average reservoir area can be assumed to be 30 km². Assume the runoff coefficient of the area flooded by the reservoir as equal to 0.4 Months Monthly inflow (×10%.m³) Monthly demand (×10%.m³) Rainfall(cm) January 50 50 1 February 40 75 0 March 30 80 0 April 25 85 0 May 20 130 0 June 30 120 19 July 200 25 43 August 225 25 39 September 150 40 22 October 90 45 6 November 70 50 2 December 60 60 1S New Two assets, Q & R, each have a standard deviation of 10%. Asset Q's expected return is 8.5% and Asset R's expected return is 7.9%. A rational investor will choose: A. Asset Q. B. Asset R. O C. Either asset R or asset Q.
- Consider an asset S with price function S = 2+2t S(t) = S=8-t for tЄ [0,2], for tЄ [2,4], St² 8t+20 for tЄ [4,6]. (a) Sketch the graph of S(t). - (b) Calculate the continuous arithmetic average of S over the interval 0 ≤ t ≤ 6. (c) Calculate the discrete arithmetic and discrete geometric average of S, where the discrete sampling points are take at times t = t; = ist for i = 0, 1, 2,...6 with St = 1. (d) What is the payoff of a European-style discrete geometric average rate call option which expires at t = T = 6 with E = 4.2? (e) What is the payoff of a European-style continuous arithmetic average strike put which expires at t = T = 6? (f) Consider a stop-loss option with λ = 5/6. At what time will this option be exercised? What will be the payoff?Each of the following questions should be answered by building a 15-period binomial model whose parameters should be calibrated to a Black-Scholes geometric Brownian motion model with: T =.25 years, S0 =100, r=2%, σ=30% and a dividend yield of c=1%. Your binomial model should use a value of u = 1.0395 and d = 1/u = 0.96201. (This has been rounded to four decimal places but you should not do any rounding in your spreadsheet calculations.) Compute the price of an American put option with strike K = 110 and maturity T = .25 years. Is it ever optimal to early exercise the put option of above?Assume the standard deviation of the market return is 0.2, the standard deviation of asset k is 0.45 and the beta of asset k is 0.675. The correlation coefficient between the return from asset k and the return from the market is: A. 0.473 OB. 0.900 OC. No answer OD. 0.290
- Suppose two asset returns are described by a two factor model, n = 0% + 11 + 1.82 + e1 2 = -1% + 2/1 + 0.52 + e2 where the volatility of first factor is 30%, the volatility of the second factor is 10%, and the correlation between the two factors is 0.5. Suppose also that the volatilities of the error terms ej and ez are both 10%. What is the covariance of n and r2 ? (Nearest 0.0001).The probability distributions of expected returns for the assets are shown in the following table: Asset A Prob Return 0.2 -5% 0.4 10% 0.4 15% a) Calculate the expected return for asset A. b) Calculate the standard deviation for asset A.Please solve very soon completely all parts
