The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function.x+0.20.075x + 0.203 ≤x≤ 5otherwise(a) Graph the pdf.0.6f(x)0.50.40.30.2f(x) =0.1O1³0.020.075x + 0.2 dx= 0.075(b) Calculate P(X ≤ 4).0.4625✓= 1.9375 --13Verify that the total area under the density curve is indeed 1.(c) Calculate P(3.5 ≤ x ≤ 4.5).0.5Calculate P(4.5 < X).0.27814+0.2x0.9375How does this probability compare to P(X < 4)?O P(X ≤ 4) < P(X < 4)P(X ≤ 4) = P(X < 4)O P(X ≤ 4) > P(X < 4)Xf(x)0.60.50.40.30.20.112345Xxf(x)0.60.50.40.30.20.1O12 345f(x)0.60.50.40.30.2XO0.1123X4 5

Given that We have to find a..Graph of pdf b..P(X≤4) c.P(3.5≤X≤4.5) P(X>4.5)

Answered: The current in a certain circuit as…

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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(c) Let X follow the gamma distribution with pdf S(z) = r(a) on z> 0. If a =1 and V(X)=4 find the value of b, and hence find E(X).
Consider a group of people who have received treatment for a disease such as cancer. Let t be the survival time, the number of years a person lives after receiving treatment. The density function giving the distribution of t is p(t) = Ce-Ct for some positive constant C, and the cumulative distribution function is P(t) = , p(x)dx. Think carefully about what the practical meaning of P(t) is, being sure that you can put it into words. a) The survival function, S(t), is the probability that a randomly selected person survives for at least t years. Find a formula for S(t). b) Suppose that a patient has a 80 percent chance of surviving at least 2 years. Find C. c) Using the value of C you found in (b), find the probability that the patient survives up to (that is, less than or equal to) 1 years. d) Using the value of C you found in (b), find the the mean survival time for patients with this survival function, in years.
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1. Develop a random variate (composition method) generator for the random variable X with the probability density function where I represents the indicator function. 5 f(x)=e*I(x 0) 4 a. Implement this generator to generate 500 random variates. b. Compute the sample mean and sample variance of these 500 variates and compare with the theoretical values. c. Plot the histogram of these 500 variates and compare the histogram with the graph of f(x).
Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel. Use the Rayleigh distribution, with pdf f(x; 0) = = e-x²/(282) 02 0 X > O otherwise as a model for the X distribution. (a) Verify that f(x; 0) is a legitimate pdf. X 02 e-x2/(202) dx = = 0 II 8 ° (b) Suppose = 110. What is the probability that X is at most 200? Less than 200? At least 200? (Round your answer to four decimal places.) at most 200 less than 200 at least 200 (c) What is the probability that X is between 100 and 200 (again assuming 0 = 110)? (Round your answer to four decimal places.) (d) Give an expression for P(X ≤ ×). P(X ≤ x) =
Let X denote the amount of space occupied by an article placed in a 1-ft3 packing container. The pdf of X is below. f(x) = 56x6(1 − x) 0 < x < 1 0 otherwise (d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.)(e) Compute E(X) and ?X. (Round your answers to four decimal places.) E(X) = ?X = (f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.)
The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. 3 ≤ x ≤ 5 f(x) = 0.025x + 0.4 0 otherwise (a) Graph the pdf. f(x) f(x) f(x) 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 1 2 3 4 5 3 Verify that the total area under the density curve is indeed 1. 150. 0.025x + 0.4 dx = = 2.3125 (b) Calculate P(X ≤ 4). How does this probability compare to P(X P(X < 4) O P(X ≤ 4) < P(X < 4) O P(X ≤ 4) = P(X < 4) (c) Calculate P(3.5 ≤X ≤ 4.5). Calculate P(4.5 < X). = X 1 4 0.6 0.5 0.4 0.3 0.2 0.1 O 1 2 3 4 X f(x) 0.6 0.5 0.4 0.3 0.2 0.1 O 1 2 3 4
a.71/36 b.71/9 c.287/72 d.179/36 e.71/144

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