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Find the expected value and variance of the random variable
X whose density function is f(x) = 1/(2(x)^0.5), 1 ≤ x ≤ 4.
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- What is the expected value of a continuous random variable X with probability density function (pdf) given by f(x) = 2x, 0 < x < 1?The length of time in hours that a rechargeable calculator battery will hold its charge is a random variable. Assume that this variable has a Weibull distribution with α=0.01 and β=2. (a) What is the density for X? (b) What are the mean and variance for X? (c) What is the reliability function for this random variable? (d) What is the reliability of such a battery at t=3 hours? At t=12 hours? At t=20 hours? (e) What is the Hazard rate function for these batteries? (f) What is the failure rate at t=3 hours? At t=12 hours? At t=20 hours? (g) Is the hazard rate function an increasing or decreasing function? Does this seem to be reasonable from practical point of view? ExplainQ3/A/ Let X be a r.v with p.d.f f(x) = e-lkl - o2x A random variable X has the density function f(x)= } k- 0, Otherwise. For what value of k the variance of X equal to 2.The pdf of random variable X is given as ƒx(x) = Find the i) Mean ii) Mean of the square [0.3507√x 0Let X ~ Uniform(a, b). Find Expected value EX.Q4) The probability mass function of Y is f(y) = y/6 for y=1,2,3,4. Find the variance of Y.A variable X has a probability function f(x, 0) = 0e 0x; x≥0 y >0. The parameter 0 is estimated using two different estimators of simple random samples of size two: 01 2x+4x2 and 2=4x+5x2 3 3 Select the best estimator for \theta by comparing the Mean Squared ErrorsRecommended textbooks for youCalculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage Learning
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