The effectiveness of solar energy heating units depends on the amount of radiation available from the sun. Fora typical month, daily total solar radiation in a community approximately follows the probability densityfunction given below (units are hundredsof calories).ƒ(x) = 32 (x − 2) (6 – x)02 ≤ x ≤ 6elsewherea. Find the probability that solar radiation will exceed 300 calories on a typical day of the month.b. What amount of solar radiation is exceeded on exactly 50% of the days of the month according to thismodel Suppose a random variable X has a probability density function given byO elsewheref (x) = kx (1 − x)0 ≤ x ≤ 10elsewherea. Find the value of k that makes this a probability density functionb. Find P (0.4 ≤ x ≤ 1)c. Find P(x ≤ 0.4)d. Find P (0.8 ≤ x))

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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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Test the following function to determine whether it is a probability function. (Give your answers correct to two decimal places.) P(x) = x2 + 5 50 , for x = 1, 2, 3, 4 (a) List the probability distribution. P(1) = P(2) = P(3) = P(4) =
Let X be the number of visits to the dentist's office for a randomly selected student. Suppose that X has a probability distribution function given by the following table: X P(X= x) 0.15 0.65 Find P(X ≤u) where µ = E(X) is the average number of visits. 0.5 0.15 1 1 0.50 2 0.35
The table shows the probability distribution of the number of days (x) to complete a construction project by a contractor. x f(x) 1 0.104 2 3 0.312 4 0.240 5 0.098 6 0.017 13 If you doubled each number of days to completion in the Days (x) column, the variance of days to completion will be _________. a 5.710 b 4.758 c 3.965 d 2.855
Let X represent the number of homes a real estate agent sells during a given month. Based on previous sales records, she estimates that P(0)= 0.62, P(1)= 0.21, P(2)= 0.13, P(3)= 0.03, P(4)= 0.01, with negligible probability for higher values of x. Find the long-term average number of homes the real estate agent expects to sell each month.
Fill in the P(X=x)values to give a legitimate probability distribution for the discrete random variable X, whose possible values are −2,1, 3, 4, and 5.
The 2010 U.S. Census found the chance of a household being a certain size. The data is in the pmf below ("Households by age," 2013). Let X be the number (size) in a household. E(X) = k·P(X = k) 7 (or more) P(X=k) 0.267 0.336 0.158 0.137 0.063 0.024 0.015 k 1 2 3 5 6 a) The probability of a household size being more than 5, P(X > 5) = % b) In the long run, we are expected to see a household size of, E(X)= on average. Round answer to three decimal places. c) The probability that the size of a household is equal to two is %. d) The probability of a household size being three OR six is %.
In each case, determine the value of the constant c that makes the probability statement correct. (Round your answers to two decimal places.) USE SALT (a) (c) = 0.9857 2.189 (b) P(0 ≤Z≤ c) = 0.3133 0.89 (c) P(C ≤ Z) = 0.1335 1.11 You may need to use the appropriate table in the Appendix of Tables to answer this question.
The probability that an event will happen isP(E)=0.22.Find the probability that the event will not happen.

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