document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136713>Question 1136713</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let X be a continuous random variable. Can the function f(x) = 2^(-x) for x > 0 and 0 otherwise be its probability density function? If so, state why. If not, explain why not. </SPAN>\n" );
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document.write( "No.<br><BR>\n" );
document.write( "The integral from 0 to infinity of f(x) = 2^(-x) is 1/ln(2) which is about 1.4427.<br><BR>\n" );
document.write( "For f(x) to be a probability density function, the integral has to be equal to 1.<br><BR>\n" );
document.write( "Note f(x) = 2^(-x) could be a probability density function if it were defined only for positive integer values of x, instead of having a continuous domain of x>0:<br><BR>\n" );
document.write( "2^(-1)+2^(-2)+2^(-3)+... = 1/2 + 1/4 + 1/8 + ... = 1. </SPAN>\n" );
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