Answered: 3. Assume that 60% of cars driven into…

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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d) The random variable X has a Poisson distribution such that P(X= 0) = P(X = 1). Calculate P(X = 2).
A certain mutual fund invests in both U.S. and foreign markets. Let x a random variable that represents the monthly percentage return for the fund. Assume x has mean u = 1.9% and standard deviation o = 0.3%. (a) The fund has over 175 stocks that combine together to give the overall monthly percentage return x. We can consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all world stocks. Then we see that the overall monthly return x for the fund is itself an average return computed using all 175 stocks in the fund. Why would this indicate that x has an approximately normal distribution? Explain. Hint: See the discussion after Theorem 6.2. The random variable -Select-v is a mean of a sample size n = 175. By the -Select- v, the -Select- distribution is approximately normal. (b) After 6 months, what is the probability that thẹ average monthly percentage return x will be between 1% and 2%? Hint: See Theorem 6.1, and assume that x has…
The probability density function of a discrete random variable X is given by the following table: Px(X = 1) = .05 Px(X = 2) = .10 Px(X = 3) = .12 Px(X = 4) = .30 Px (X = 5) = .30 Px (X = 6) = .1i Px (X = 7) = .01 Px(X = 8) = .01 i) Compute E(X). ii) Compute Var(X). iii) Compute Px(X 3)
If X is normally distributed with mean 0 and variance 1, what is the probability density function of X2 ?
1. Determine the constant c so that the function p(x) = 0(x) defines the probability den- sity for a random variable {. Then find the cumulative distribution function and the mean of {. %3D
2. Customers purchase a particular make of automobile with a variety of options. The probability mass function of the number of options selected is x 7 8 9 10 11 12 13 f(x) 0.04 0.13 0.19 0.24 0.3 0.05 0.05 Consider customers that chose at most 9 options, which proportion of these cus- tomers chose 7 options? (A) 11.11% (B) 4% (C) 5.65% (D) 13% (E) 5%
A product is classified according to the number of defects, it contains (X1) and the factory that produces it (X2),. The joint probability distribution is given by X/X2 2 0 1/8 1/16 I/16 1/16 3/16 1/8 3 1/8 1/4 (a) Find the marginal distribution of X1
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(a). Derive the theorem of total chance of occurrence of engineering events. (b). If Faculty of Engineering and Technology is located south of the land of Malete and experiences Wet and Dry seasons yearly. Assume the Wet season in the vicinity of the building lasts for 1/3 of the year, and the Dry season for 2/3 of the year. The chances of rain falling during the wet and dry seasons are 3/4 and 1/6, respectively. i. If you visit the engineering building on a random day of the year, what is the chance that it will rain on arrival? If you visit the engineering building on a random day, and it rains on arrival. What is the chance that your visit is during the wet season? ii.
Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.33 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. (a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your answers to four decimal places.) 0 1 2 3 4 5 6 7 8 P(X=x) 0 1 2 3 4 5 6 7 0.1350 0.1330 0.2322 0.1965 0.2633 ✓ ✔ (b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.) F(x) 0.1350 0.268 0.5002 0.6967 x

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X	1	2	3	4	5
P(X=x)	0.60	0.20	0.12	0.06	0.02