Let x be uniformly distributed on an interval (say [-1,1]). Let y = w1 x1 + w2 x2 + ... + wn xn be a weighted average of random variables x1,x2,...,xn which themselves are independent and identically distributed draws from the distribution of x. Let the weights wi, i = 1,...,n, sum to 1, and satisfy the bounds 0 < wi < 1.
Conjecture: The random variable y has a probability density function which is a polynomial spline function of order n-1. Is this conjecture true, and if so, are there known closed-form (in terms of w, n) solutions for the density of y? -- Scott Gilbert Economics Department, MC4515 Southern Illinois University at Carbondale Carbondale, IL 62901-4515 phone: (618) 453-5065 fax: (618) 453-2717 e-mail: [EMAIL PROTECTED] . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
