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- For the given probability density function, over the given interval, find the mean, the variance, and the standard deviation. 36) f(x)== // [12, 20] 36) B) μ = 16; o² = 5.33; o = 2.31 A) μ = 15.5; o2=5.20; o = 2.28 C) μ = 15; o2 = 5.34; o = 2.31 D) μ= 1.6; o2 = 5.24; o=2.29Let the random variable X has probability density function given by x2-2x+2 03. If the probability density function of random variable is given by f(x)=1/sechx 1 ≤ x ≤ 2 a) Find the mean b) Find the total areaA scout on a camping trip is requested to find some dry sticks of length at most one metre to use as firewood. A model for the distribution of the lengths, X, in metres, of sticks that she brings back to the camp has probability density function f(x) = VT, 0< x < 1. 0 < x < 1. According to the model, what is the mean length of the sticks that the scout brings back?According to a study, the maximum temperature T (in degrees Celsius) of each day during the spring has a distribution with the following function density: 21Please answer number 4For a random variable which can be defined using the probability density function below, what is the probability that X is between 1.3 and 3.1? с (1 + х) ,1 <Question 2. A continuous random variable, X has the following probability density function: S(x) = cx² 0sxs10 = 0 otherwise a) Find the value of c. b) Find the mean, median, mode, standard deviation and coefficient of variation. c) Find the probability that X is greater than 3.0 given that X is between 2.0 and 5.0.1. Each rear tire on an experimental airplane is supposed to be lled to a pressure of 40 pounds per square inch (psi). Let Y1 denote the actual air pressure for the right tire and Y2 denote the actual air pressure for the left tire. Suppose that Y1 and Y2 are random variables with the joint density function attached as a photo. a) Find k. b) Find the joint distribution function for Y1 and Y2. c) Find the probability that both tires are underfilled.An article suggests the uniform distribution on the interval from 6.5 to 19 as a model for x = depth (in centimeters) of the bioturbation layer in sediment for a certain region. (a) What is the height of the density curve? (b) What is the probability that x is between 10 and 14? P(x is between 10 and 14) = Between 13 and 17? P(x is between 13 and 17) = You may need to use the appropriate table in Appendix A to answer this question.The density function of the continuous random variable X is shown below. When c≈ 0.163, Find: (1) the mode, (2) the median, and (3) the mean. Jcsin (2 -0.2x) for 1≤ x ≤ 10 f(x) = {0 elsewhere mahamdy@uoanbar.edu.iqQ2. The duration of a construction activity was estimated to be in the range [2, 6] days with a most likely duration of 4 days. A construction engineer used the following symmetric density function to model the duration: fx(x) = 12 8 12 X 12' for 2 ≤x≤4 for 4 ≤x≤6 Determine the (a) mean, (b) variance, (c) standard deviation, (d) coefficient of variation, and (e) skewness.SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON