Suppose your expectations regarding the stock market are as follows:State of the EconomyBoomNormal growthRecessionProbability0.30.50.2MeanStandard deviationHPRE (r) = Σ₁_₁ p (s)r (s)Var (r) = o² = Σ₁-1 p (s)[r(s) - E (r)]²SD (r) = o = √/Var (r)Required:Use above equations to compute the mean and standard deviation of the HPR on stockRound your answers to 2 decimal places.)%%36%18-12

Solution-:Given table:State of the EconomyProbability HPRBoom0.336%Normal…

Answered: Suppose your expectations regarding the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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a) A university projects that enrollments are going to decline as the pool of college-aged applicants begins to shrink. They have estimated the number of applications for coming years to behave according to the function a = f(t) = 6,500 – 250t where a equals the number of applications for admission to the university and t equals time in years measured from this current year (t = 0). i. What class of function is this? ii. What is the expected number of applications 5 years from today? 10 years? iii. Do you think this function is accurate as a predictor indefinitely into the future? iv. What kinds of factor would influence the restricted domain on t?
Vanessa has a utility function for income given by U(I) = VI %3D (that is the square root of income). Because of the nature of her utility function, we know that Vanessa is risk averse. Vanessa is considering an investment that would give her an income of $10,000 with a probability of 0.5 or an income of $15,000 with a probability of 0.5. The expected utility of this investment is (rounded to 2 decimal places): O A. 111.24 O B. 113.48. O C. 118.35. O D. 125.00.
You test some components with a Weibull distribution at temperatures of 100 Celcius and 60 Celcius. At those temperatures you estimate a characteristic life of 15000 hours and 25000 hours respectively. hint: Boltzmann's constant is k = 8.617 x 10-5. Temperature in Celcius + 273.15 = temperature in Kelvin. If n is an integer, T(n) = (n – 1) a) Using linear regression, estimate the Arrhenius model parameters A and AH. b) Give the MTTF, median, and 90th percentile at T = 20 Celcius. Assume that the shape parameter is 0.5
A technician discovered that the cumulative distribution function (CDF) of the lifespan of bulb in years is given by f(y) = -10 ye 10 100 0
1. You have the following PDF: f(x) = { 1≤x≤e. (a) Find the value of c such that this is a valid PDF. (b) Calculate E(X). (c) Calculate V(X). (d) Calculate F(x).
5
2. Determine whether each of the following distributions are exponential family. For those that are, find a set of complete, minimum sufficient statistics. For those that are not, find a sufficient statistic. (a) Location Exponential: f(x) = e-(-0), x > 0. (b) f(x) = 0(1+x)(1+0), x > 0 (c) logN(u,02): f(x) = 1 a exp{-(log x-μ)²), x > 0. αν2πσ2 },
1. Suppose that the PDF of X is given by 1+0.4x2 0< x <1 f(x) otherwise a. Find the expected value of X, E(X). b. Find the variance of X, Var(X). c. Find the standard deviation of X, Std(X)
1. Fix r € N, and suppose that Y₁,..., Yn are independent and identically distributed NegBin(r, ) random variables, each with probability mass function given by ¡v (u | 0) – (1 + r − ¹) (1 - fy y (1 - 0) ³0⁰ for y ¤ N and unknown 0 € (0, 1). Here the number of successes r in the negative binomial is known.
If X has the exponential distribution given by: f(x) = 4*(1 - x/2); 1 ≤ x ≤ 2. Find E(x).
Evaluate the following; show complete solutions. (Gamma Distribution)
Directions: Suppose that the average life span of an electronic component is 72 months and that the life spans are exponentially distributed. 1. Find the probability that a component lasts for more than 12 months. Probability= 0.846482 2. The reliability function r(t) gives the probability that a component will last for more than ₺ months. Compute r(t) in this case. r(t) = e 12

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