If x is a continuous random variable, then _____. A) the probability that x is negative is zero B) the probability that x lies in an interval is an area under the density function C) x has a normal distribution D) the expected value of x is less than the standard deviation of x
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If x is a continuous random variable, then _____.
A) the probability that x is negative is zero
B) the probability that x lies in an interval is an area under the density
C) x has a
D) the
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- X is a continuous random variable and its density function is 0 ≤ x ≤ 1, f₂(x) = {} x ‡ {0 ≤ x ≤ 1}. What is k ? O a. 1 O b. 1.5 O c. 2 O d. 3 e. 4 kxThe probability density function (p.d.f.) of a continuous random variable X is defined to be: kx + for 0 < x < 1 f(x) = |0 otherwise, for some constant k. For these problems, please ensure your answers are accurate to within 3 decimals. Part a) Find the value of k that makes the above function a proper p.d.f. Part b) Find E(X).For the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the random variable x is within one standard deviation of the mean. 1 f(x) = x, [2,4] ..... a) Find the mean. (Round to three decimal places as needed.) b) Find the standard deviation. O = (Round to three decimal places as needed.) c) Find the probability that the random variable x is within one standard deviation of the mean. The probability is (Round to three decimal places as needed.)
- Let X luck variable with exponential distribution have a density function f(x) = 0.5e-0,5∞x> 0. In this case, determine the probability P (2 <X <2.5) for the mean of the chance sample with a width of n = 36 selected from the relevant distribution by the normal distribution approach. a) 0.567 b)0.933 c)0.466 d)0.433 e)0.067The probability density of a random variable X is given in the figure below. 1 2. a) Write the density function of X: f(z) = 08. If X is uniformly distributed over (–1,1), find a. P(\X|>;) b. Density function of the random variable |X].A continuous random variable Z has a probability density function f(z) = Find the following: a) P(Z > 1.2) b) P(0.6 ≤ Z≤ 1) (0.25z³, 0≤x≤ 2 (0, elsewhereNumber...3...QUES a) Suppose that a random variable X has a probability density function of the form 9 f(x) = {kx² (1-x) ³, 0 < x < 1 1) ii) What is the distribution of X? What is the value of k? 0, elsewhere 2 in pomatric. DorLet X be a random variable with a uniform distribution on the interval (0,1). Given Y = e*, derive a) b) the probability distribution function of Y = ex. the probability density function of Y.|A 9 a) The continuous random variable Xhas probability density function f (x) = 0(1– x)"-1 , 0 0 i) Find the cumulative distribution function, F(x), of X ii) Find P(0.255. Let X be a random variable with a uniform distribution on the interval (0,1). Given Y = e, derive a) b) the probability distribution function of Y = e*. the probability density function of Y.SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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