The CDF of X is given in the following function: The cumulative distribution function of X...
4. Cumulative distribution function (cdf) of a random variable X is given by 1t2 2 Find a) Pdf of X and b) ECX3-2 IXI).
For a random variable X with cumulative distribution function (cdf) Fx(x) = 1- (2/x)^2 ,x>2. (a).Find the pdf fX(x). (b).Consider the random variable Y = X^2. Find the pdf of Y, fY (y).
Suppose that X is a random variable whose cumulative distribution function (cdf) is given by: F(x) = Cx -x^2, 0<x<1 for some constant C a. What is the value of C? b. Find P(1/3 < X < 2/3) c. Find the median of X. d. What is the expected value of X?
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0 if x < 0 0.2 if 0 < x < 1 Ex(x) = {0.5 if 1 < x < 2 0.9 if 2 < x <3 11 if x > 3 a)Give the probability mass function of X, explicitly. b) Compute P(2 < X < 3). c) Compute P(x > 2). d) Compute P(X21|XS 2).
1. A certain continuous distribution has cumulative distribution function (CDF) given by F(x) 0, r<0 where θ is an unknown parameter, θ > 0. Let X, be the sample mean and X(n)max(Xi, X2,,Xn). (i) Show that θ¡n-(1 + )Xn ls an unbiased estimator of θ. Find its mean square error and check whether θ¡r, is consistent for θ. (i) Show that nX(n) is a consistent estimator of o (ii) Assume n > 1 and find MSE's of 02n, and compare...
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4. Let X be a random variable with the following cumulative distribution function (CDF): y <0 F(y) (a) What's P(X 2)? b) What's P(X > 2)? c) What's P(0.5<X 2.5)? (d) What's P(X 1)? (e) Let q be a number such that F()-0.6. What's q?
Let X be a random variable with the following cumulative distribution function (CDF): y<0 (a) What's P(X < 2)? (b) What's P(X > 2)? c)What's P(0.5 X < 2.5)? (d) What's P(X 1)? (e) Let q be a number such that F(0.6. What's q?
Let X be a random variable with probability density function (pdf) given by fx(r0)o elsewhere where θ 0 is an unknown parameter. (a) Find the cumulative distribution function (cdf) for the random variable Y = θ and identify the distribution. Let X1,X2, . . . , Xn be a random sample of size n 〉 2 from fx (x10). (b) Find the maximum likelihood estimator, Ỗmle, for θ (c.) Find the Uniform Minimum Variance Unbiased Estimator (UMVUE), Bumvue, for 0...
Define the random variable Y = -2X. Determine the cumulative
distribution function (CDF) of Y . Make sure to completely specify
this function. Explain.
Consider a random variable X with the following probability density function (PDF): s 2+2 if –2 < x < 2, fx(x) = { 0 otherwise. This random variable X is used in parts a, b, and c of this problem.
Figure out if the following graph can be a "Cumulative Distribution Function (CDF)". If it can, select whether the variable is "Discrete" or "Continuous". (vii) ↑F'(x) Vil 0.5 AC O A. Discrete B.Continuous ° C. Cannot be a CDF