Suppose you have some money to invest-for simplicity, $1-and you are planning to put a fraction w into a stock market mutual fund and the rest, 1 - w, into abond mutual fund. Suppose that $1 invested in a stock fund yields R, after 1 year and that $1 invested in a bond fund yields R, suppose that R, is random withmean 0.08 (8%) and standard deviation 0.07, and suppose that R, is random with mean 0.05 (5%) and standard deviation 0.04. The correlation between R, andR, is 0.24. If you place a fraction w of your money in the stock fund and the rest, 1 - w, in the bond fund, then the return on your investment is R= wR, + (1- w)R,.Suppose that w= 0.48. Compute the mean and standard deviation of R.The mean is 064 . (Round your response to three decimal places.)The standard deviation is 0436 . (Round your response to three decimal places.)Suppose that w= 0.71. Compute the mean and standard deviation of R.The mean is(Round your response to three decimal places.)The standard deviation is. (Round your response to three decimal places.)

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Answered: Suppose you have some money to…

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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Suppose that half of all students (50%) in campus dormitories are dissatisfied with the food service. A random sample of 64 students was taken. What is the probability that the number of students in the sample who were dissatisfied with the food service was between 30 and 34 (inclusive)? (Use the normal approximation to the binomial distribution, without the continuity correction.).
Suppose 500 people audition for admission to a dance school. Each dancer in one half of the group will be admitted with probability 0.07, while each dancer in the other half of the group will be admitted with probability 0.04. Let X be the total number of dancers admitted. (Notice that X is the sum of two binomial variables). (a) Find the mean and variance of X. (b) Use normal approximations to binomial random variables to approximate (i) the probability that more than 30 dancers are admitted. (ii) the probability that at least 20 dancers are admitted.
Suppose that a new detection tool is introduced starting in week 3 and that from week 3 onwards, each fake bill has a 1 in 3 chance of being detected at each transaction. In this case, what is the totalexpected number of times that the fake bills are successfully used in transactions without being detected?
5. Prove that the mean of Binomial Distribution is np and the variance is np(1 – p).
5. Suppose that a student attending a class has an infectuous disease. Suppose that with probability 1/2 she does not infect anybody, with probability 1/4 she infects exactly one other person, and with probability 1/4 she infects exactly two people. Let X be the number of people infected by this student. Calculate the expectation and the variance of X.
1.A family wishes to adopt 4 pets from a total of 13 dogs and 7 cats available at an animal shelter. The variable "x" being measured is the number of dogs. Show the probability distribution table, using 3 columns: one for x, one for P(x), and one for x*P(x). The second column should show calculations using C(Dt). 2. A student forum at a high school needs to elect 5 people from 10 Grade 11 students and 15 Grade 12 students who are available. The variable"" being measured is the number of Grade 12 students. Show the probability distribution table, using 3 columns: one for x, one for P(x), and one for x*P(x). The second column should show calculations involving C(Dt).
In studies for a medication, 7 percent of patients gained weight as a side effect. Suppose 565 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that (a) exactly 40 patients will gain weight as a side effect. (b) no more than 40 patients will gain weight as a side effect. (c) at least 51 patients will gain weight as a side effect. What does this result suggest? (a) P(40) = (Round to four decimal places as needed) (b) P(X< 40) = (Round to four decimal places as needed) (c) P(X251) = (Round to four decimal places as needed) Since 51 is than 7% of the patients, this suggests that the proportion of patients that gain weight as a side effect is 0.07.
Suppose the demand for a company’s product in week 1,2, & 3 are each normally distributed. The means are 50, 45, and 65. The standard deviations are 10,5, and 15. Assume these 3 demands are probabilistically independent. Suppose the company has 180 units in stock, and it will not be receiving any more shipments from its supplier for at least 3 weeks. What is the probability that stock will run out during the 3 week period? How many units should the company have in stock, so that it can be 98% certain of not running out during the 3 week period , assuming it will not receive any more shipments during this period?
What is the probability of getting at least one tail if two unbiased coins are independently tossed? а. 1/4 b. 1/2 с. 7/8 d. 3/4
Suppose that 2% of transactions in a region are fraudulent. Transactions are assumed to be independent of each other. Calculate with the help of the normal approximation that between 1000 More than 20 transactions are fraudulent. Show your work.
A bank has 3 counter desks and a very large waiting lounge (assume infinite queue). Customers arrive with a mean of 20 per hour and each desk serves with mean 10 customers per hour, where both rates are exponential. Determine the following : (a) Determine An, tn, C, and Aeff for n = 0, 1, 2, 3... (b) The steady-state probabilities pn,n = 0, 1, 2, 3.. (c) Calculate steady-state measures Ls, Ws, Lg, Wq, c and utilization ratio.
One year consumers spent an average of $22 on a meal at a resturant. Assume that the amount spent on a resturant meal is normally distributed and that the standard deviation is $3.Complete parts (a) through (c) below. a. What is the probability that a randomly selected person spent more than $24?

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