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 October 23rd, 2015, 04:30 AM #1 Newbie   Joined: Jan 2014 Posts: 10 Thanks: 0 Description of distribution w. indicator random variable Dear Forum, I was discussing this very interesting problem with my friend, and I want to hear your opinions on it. Let $\displaystyle X$ be a random variable with unknown distribution, and $\displaystyle c$ be a user-define parameter. Let $\displaystyle A$ be the event that $\displaystyle X = x \leq c$ Define the random variable $\displaystyle Y$, such that $\displaystyle Y = y = g$ if $\displaystyle A$ occurs and $\displaystyle Y = y = 0$ otherwise. How do i give a formal distribution of $\displaystyle Y$, i.e. expected value and variance? If the general case is too difficult, we can assume that $\displaystyle X$ is normally distributed October 23rd, 2015, 04:33 PM #2 Global Moderator   Joined: May 2007 Posts: 6,768 Thanks: 699 Since Y has only two possible values (g or 0) it cannot be normally distributed. Since the distribution for X is unknown, you can't say much about the distribution for Y. October 25th, 2015, 03:57 AM   #3
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 Originally Posted by mathman Since Y has only two possible values (g or 0) it cannot be normally distributed. Since the distribution for X is unknown, you can't say much about the distribution for Y.
The OP was saying we can assume X, not Y, is normally distributed... in which case the distribution for X is known. October 25th, 2015, 07:12 PM #4 Global Moderator   Joined: May 2007 Posts: 6,768 Thanks: 699 Sorry to have misread the question. The distribution for Y, even if X is normal, will be determined by the mean and variance for X. October 26th, 2015, 08:23 AM #5 Senior Member   Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics If $\displaystyle X \sim N(\mu, \sigma^2)$ and the c-parameter is $\displaystyle \mu$, then $\displaystyle Y \sim Bernoulli(0.5)$ and thus $\displaystyle E(Y) = 0.5$ and $\displaystyle Var(Y) = 0.5(1-0.5) = 0.25$. Not exactly groundbreaking, though :P Tags description, distribution, indicator, probability, random, variable Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post r-soy Algebra 6 October 11th, 2017 07:58 AM wonderlex Probability and Statistics 0 May 16th, 2014 09:43 PM frankpupu Advanced Statistics 2 March 1st, 2012 03:45 AM fin0c Advanced Statistics 1 January 23rd, 2011 10:43 PM alfangio Advanced Statistics 1 March 17th, 2009 01:46 PM

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