document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=762057>Question 762057</A>: <I><SPAN STYLE=\"word-break: break-all;\">  i would be glad if you could help check if my answers are correct<BR>\n" );
document.write( "Consider the following discrete probability distribution function for the variable X:<BR>\n" );
document.write( "x<BR>\n" );
document.write( "10<BR>\n" );
document.write( "12<BR>\n" );
document.write( "14<BR>\n" );
document.write( "16<BR>\n" );
document.write( "18<BR>\n" );
document.write( "f(x)<BR>\n" );
document.write( ".02<BR>\n" );
document.write( ".7<BR>\n" );
document.write( ".05<BR>\n" );
document.write( ".2<BR>\n" );
document.write( ".03 P.s this is a table showing corresponding values of x and f(x)\r<BR>\n" );
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document.write( "a)  Is this a proper probability mass function? How do you know?\r<BR>\n" );
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document.write( "b)  What is the probability that any draw from this distribution, say X, is less than 16 [i.e. find P(X<16)]?\r<BR>\n" );
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document.write( "answers i arrived at but not sure about them yet;\r<BR>\n" );
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document.write( "Yes this is a proper probability mas function because 0 < f(x) &#8804; 1 and the sum of all the f(x)values is 1\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "The formula for probability is as follows;<BR>\n" );
document.write( "P (E) =  The Number Of Ways Event can occur/The total number Of Possible Outcomes\r<BR>\n" );
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document.write( "The probability that P(X<16) = Number of X values less than 16/The total number of values<BR>\n" );
document.write( "According to the table the number of values less than 16 is 3 (i.e. 10, 12, 14) and the total number of values is 5<BR>\n" );
document.write( "Therefore The probability that P(X<16) = 3/5 =0.6\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #463681 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=463681\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider the following discrete probability distribution function for the variable X:<BR>\n" );
document.write( "x<BR>\n" );
document.write( "10<BR>\n" );
document.write( "12<BR>\n" );
document.write( "14<BR>\n" );
document.write( "16<BR>\n" );
document.write( "18<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "f(x)<BR>\n" );
document.write( ".02<BR>\n" );
document.write( ".7<BR>\n" );
document.write( ".05<BR>\n" );
document.write( ".2<BR>\n" );
document.write( ".03 <BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "P.s this is a table showing corresponding values of x and f(x) <BR>\n" );
document.write( "a) Is this a proper probability mass function? How do you know?<BR>\n" );
document.write( "Each probability is between -1 and +1 <BR>\n" );
document.write( "The sum of the probabilities = 1<BR>\n" );
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document.write( "b) What is the probability that any draw from this distribution, say X, is less than 16 [i.e. find P(X<16)]?<BR>\n" );
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document.write( "Ans: 0.02+0.70+0.05 = 0.75<BR>\n" );
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document.write( "answers i arrived at but not sure about them yet; <BR>\n" );
document.write( "Yes this is a proper probability mas function because 0 < f(x) &#8804; 1 and the sum of all the f(x)values is 1 \r<BR>\n" );
document.write( "\n" );
document.write( "The formula for probability is as follows;<BR>\n" );
document.write( "P (E) = The Number Of Ways Event can occur/The total number Of Possible Outcomes <BR>\n" );
document.write( "The probability that P(X<16) =  0.02+0.70+0.05 = 0.75<BR>\n" );
document.write( "===============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "====================\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );