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\n" ); document.write( "Question:
\n" ); document.write( "Find the expected value for the probability distribution in the table below.
\n" ); document.write( "Value Probability
\n" ); document.write( "0 0.15
\n" ); document.write( "1 0.2
\n" ); document.write( "2 0.1
\n" ); document.write( "3 0.25
\n" ); document.write( "4 0.3
\n" ); document.write( "
\n" ); document.write( "Solution:
\n" ); document.write( "For a given probability distribution p(x), the expected value is given by
\n" ); document.write( "E[X]=∑x*p(x) over the valid values of x.
\n" ); document.write( "For the given distribution
\n" ); document.write( "X P(X)
\n" ); document.write( "0 0.15
\n" ); document.write( "1 0.2
\n" ); document.write( "2 0.1
\n" ); document.write( "3 0.25
\n" ); document.write( "4 0.3
\n" ); document.write( "We calculate ∑x*p(x) = 0*0.15+1*0.2+2*0.1+3*0.25+4*0.3=2.35
\n" ); document.write( "So the expected value of the distribution is 2.35.
\n" ); document.write( " \n" ); document.write( "