1. Suppose that X is a random variable with pdf: f(x) = (2x + 1)/6, 0 < x < 2. (a)Find the cdf . Give the complete cdf for any real value of x. (b)Find the mean and variance of X. (c)Verify that Chebyshev’s Theorem holds for k = 5/3. (d) Find P(0.10 < X < 0.50) using the cdf in (a).
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#1.
Suppose that X is a random variable with
(a)Find the cdf . Give the complete cdf for any real value of x.
(b)Find the mean and variance of X.
(c)Verify that Chebyshev’s Theorem holds for k = 5/3.
(d) Find P(0.10 < X < 0.50) using the cdf in (a).
Step by step
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- 2Consider a continuous random variable X with the pdf 0 < x < 1 f(x) = { J x, c/x°, 1 < x <∞ Find (a) The value of c so that f (x) is a pdf. (b) The mean of X (if it exists). (c) The variance of X (if it exists). (d) P(1/2 < X < 2) (e) T.82.Given (x + 2y) ,0Let X = (X1, X, )" be a bivariate random variable with variance-covariance matrix 4 -1.5 E(X – E(X))(X – E(X))") = ( -1.5 1 You are given that X1 + aX2 is independent of X1. Find the number a. Give your answer in 2 decimal places. Answer:3. Let the random variable X have the moment generating function M(t) = What are the mean and the variance of X, respectively? -1 < t < 1.8. Let the random variable X have the pdf 2 x2 fx (x) = exp %3D - V2n 2 Find the mean and the variance of X. Hint: Compute E (X) directly and E (X²) by comparing the integral with the integral representing the variance of a random variable that is N(0,1). i DCO 04 < (X - 5)2 < 38.4).Let Y < Y, < Y3 be the order statistic of a random sample of size 3 from the uniform distribution having pdff (x;0) = 1/0,0(b) Consider the generalised three-parameter beta distribution with pdf 121?x (1 – x)² [1- (1 – 2) x]5* fx (x) = 04. Assume that X is an exponential random variable. Suppose further that Var(X) = 5. E(X). (a) Find the parameter 0> 0. (b) Compute Var(X + 4). (c) Compute P(X > 15[X > 11).Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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