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- In a certain experiment, the error made in determining the density of a substance is evenly distributed between -0.0015 and 0.0015. Find the probability that such an error will exceed 0.0005 in absolute value. 11.Gggnnnnvariable has the density curve whose equation is ? = 2x for 0 < ? < 1, and ? = 0 otherwise. d) What percentage of all possible observations of the variable are at most 3/8? e) What percentage of all possible observations of the variable are at least 1/4? f) What percentage of all possible observations of the variable lie between 1/2 and 3/4?
- The length of time, in minutes, for an airplane to obtain clearance for takeoff at a certain airport is a random variable Y = 5X-4, where X has the following density function. Find the mean and variance of the random variable Y. 1 f(x)=2' X 2 x>0 0, x≤07.1 Let X be a random variable with probability Si. 1= 1,2, 3, S(2) =10 elsewhere. Find the probability distribution of the random vari- able Y = 2X 1. 7.8 A dealer's profit, in units of $5000, on a new au- tomobile is given by Y = X², where X variable having the density function sa random S(z) =2(1 - 2), 0The probability density function of a random variable Y is given by 24y(10+2y- 0.3y²) S; (y)=< 0 < y<10 10000 0, otherwise Suppose a random sample of 40 observations is obtained from this distribution and these are denoted as Y,,Y,,…,Y40 • 40 a) Approximate the probability that the sample sum T =Ey, is between 200 and 250. i=1 b) Approximate the probability that the sample mean Y is less than 5.5.Suppose that the random variable X has density function fx (x) = bx°-1 for 0 < x < 1, where b is a constant. If the median of X is 0.4, what is the value of the constant b?A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X be the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is fo fkr², if 0Assume that x,, . .. , Xn are the realization of the random samples X, ... , Xn with pdf or pmf fo. Find the UMP of Ho : 0 = 0 versus H, : 0 = 0, . for 0, > 0o fe(x) is density of normal with mean 0 and known o. fe(x) is density of normal with known mean u and variance 0 = o² .The value of the random variable X is from the unit disc D {(x, y) | < 1}distance of a randomly chosen (ie density function = constant x² + y² = 1/A) point from the origin. Calculate its expected value EX = = = √ √ √₁₂ √x² + y² dA. =B1. Let us consider a random variable X following a Weibull distribution with parameter k = 2 and A > 0, which has density function Se-/A)", if x2 0, 0, fx(x) otherwise. Given the following random numbers sampled from the uniform distribution on the interval [0, 1], u1 = 0.1345, u2 = 0.7515, uz = 0.1671, u4 = 0.9101 and uz = 0.0578; compute five sampled values for X for A = 3.2.5 Y has a density function S0) = (2 y), 0 < y < 2 elsewhere Find the mean and variance of Y.Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON