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- f(X)= 3/8( 4x - 2x2 ) 0<* x <* 2 (* less or equal to) a. Find the variance of X.If X is a random variable with pdf f(x) = 2x − 2 where x = (1, 2), find the variance of Y = 2X - 3.The CDF F(x) of a random variable X is given by;F(x) = { 0 , ?? ? ≤ 1 ? (? − 1)^4 , ?? 1 < ? ≤ 3 1 , ?? ? > 3} find PDF f(x) (ii) ?(|?| < 1.5), (iii) the mean and variance of X.
- If X has an exponential distribution, show thatP[(X Ú t + T)|(x ÚT)] = P(X Ú t)B1. Let X be a continuous random variable with PDF 2 f(x) = ½ ½ (2 - x) 9 and f(x) = 0 otherwise. for 1x c (a) Explaining your work, find the value of the constant c. (b) What is P(X > 1)? (c) Calculate the expectation of X. (d) Calculate the variance of XSuppose X is a random variable, whose pdf is defined as follows: 2x = (²x) (u(x) - u(x − 3)) where u(x) is the unit step function. Determine the conditional pdf fx(x 1IF it was XG (23) Independent of Xen G (13) Find Miley D-Probability density Function of the Variable YaX+Xq 2 -the Mean variance of the variableExpress var(X + Y), var(X − Y), and cov(X + Y, X −Y) in terms of the variances and covariance of Xand Y.68. Let X be a continuous random variable with pdf (a) Find the pdf for Y = √X. (b) Find the pdf for U = ln X. fx(x) = 3x²I(0,1)(x)If random variable x is exponentially-distributed with mean A =2, calculate P(X>3): 2 2e-2x x = 3 3 2 2e-2x X = 0 | 2e-2x dx | 3e-3*dx 2 3e-3x X = 2 .3 | 2e-2xdxIF it was XG (23) Independent of Xen G (13) Find Miley D-Probability density Function of the Variable Y-X+Xq 2 -the Mean variance of the variableSuppose the random variable T is the length of life of an object (possibly the lifetime of an electrical component or of a subject given a particular treatment). The hazard function hr(t) associated with the random variable T is defined by hr(t) = lims-o- P(t ≤ TSEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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