Consider a discrete random variable, X, having pmf pX(x) = (1 )^.pdf
0 likes5 views
The document discusses a discrete random variable, x, with a specific probability mass function. It provides a method to express the expectation E(x) simply as a function of a parameter ?. The solution involves differentiating and performing algebraic manipulations to derive the final expression for E(x).
1 of 1
Download to read offline
More Related Content
More from alamodeindia1 (6)
Recently uploaded (20)
Consider a discrete random variable, X, having pmf pX(x) = (1 )^.pdf
- 1. Consider a discrete random variable, X, having pmf pX(x) = (1 ? ?)?^x I{0,1,2,...}(x). Give a simple expression for E(X), expressing the expectation as a very simple function of ? Solution E(x) = x.p(x) = x(1-)^x We have: ^x = 1/(1-) Differentiate: x.^(x-1) = 1/(1-)^2 Multiply by : x.^x = /(1-)^2 Therefore: E(x) = x(1-)^x = (1-)*/(1-)^2 = /(1-)