document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193219>Question 1193219</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have done i,ii,iii just need v but unsure if right \r<BR>\n" );
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document.write( "The random variable 𝑋 is given by the sum of the scores when two ordinary dice are thrown. For this experiment:<BR>\n" );
document.write( "i) Write down the sample space 𝑆.<BR>\n" );
document.write( "ii) Draw a table to show the probability distribution and the cumulative<BR>\n" );
document.write( "distribution of 𝑋.<BR>\n" );
document.write( "iii) Write down the probability function of 𝑋.<BR>\n" );
document.write( "iv) Draw a vertical line graph to illustrate the probability distribution of 𝑋(with probability on the y-axis and 𝑋- values on the x-axis) and describe the shape of the distribution. (You may use excel or simply draw by hand on paper)<BR>\n" );
document.write( "v) Evaluate the following. You must show your working (you may use Excel where possible to show working)<BR>\n" );
document.write( "1. 𝑃(𝑋>8)<BR>\n" );
document.write( "2. 𝑃(|𝑋−7|<3)<BR>\n" );
document.write( "3. 𝐸(𝑋)<BR>\n" );
document.write( "4. 𝑉𝑎𝑟(𝑋)\r<BR>\n" );
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document.write( "A.i)							<BR>\n" );
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document.write( "Dices	1	2	3	4	5	6	<BR>\n" );
document.write( "1	1,1	1,2	1,3	1,4	1,5	1,6	<BR>\n" );
document.write( "2	2,1	2,2	2,3	2,4	2,5	2,6	<BR>\n" );
document.write( "3	3,1	3,2	3,3	3,4	3,5	3,6	<BR>\n" );
document.write( "4	4,1	4,2	4,3	4,4	4,5	4,6	<BR>\n" );
document.write( "5	5,1	5,2	5,3	5,4	5,5	5,6	<BR>\n" );
document.write( "6	6,1	6,2	6,3	6,4	6,5	6,6	sample space = 36\r<BR>\n" );
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document.write( "ii.	X	1	2	3	4	5	6<BR>\n" );
document.write( "	P(X=x)	 1/36	 3/36	 5/36	 7/36	 9/36	 11/36<BR>\n" );
document.write( "	P(x)	 1/36	 4/36	 9/36	 16/36	 25/36	1\r<BR>\n" );
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document.write( "iii.<BR>\n" );
document.write( "P(X=x) 	{1/36 	x = 1<BR>\n" );
document.write( "	 3/36	x = 2<BR>\n" );
document.write( "	 5/36	x = 3<BR>\n" );
document.write( "	 7/36	x = 4<BR>\n" );
document.write( "	 9/36	x = 5<BR>\n" );
document.write( "	 11/36	x = 6.       this right ??\r<BR>\n" );
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document.write( "v. is here but unsure if is right\r<BR>\n" );
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document.write( "											7	8	9	10	11	12<BR>\n" );
document.write( "v.											13/36	15/36	17/36	19/36	21/36	23/36<BR>\n" );
document.write( "1							𝑃(𝑋>8) =  	P ( X≥9) 	F(9) =2.25		49/36=1.36	64/36=1.78	81/36=2.25	100/36=2.78	121/36=3.36	144/36=4<BR>\n" );
document.write( "2							𝑃(|𝑋−7|<3)									<BR>\n" );
document.write( "3							𝐸(𝑋)= 10.63		x	p(x)	xp(x)	x^2 p(x)	(x-m)^2P(X)			<BR>\n" );
document.write( "							or 4.472		1	0.027	0.27	0.03				<BR>\n" );
document.write( "4							Var(x) =71.001216		2	0.11	0.22	0.44				<BR>\n" );
document.write( "							1^2=1		3	0.25	0.75	2.25				<BR>\n" );
document.write( "							2^2=4		4	0.44	1.76	7.04				<BR>\n" );
document.write( "							3^2=9		5	0.69	3.45	17.25				<BR>\n" );
document.write( "							4^2=16		6	1	6	36				<BR>\n" );
document.write( "							5^2=25			∑p(x)=2.52	∑xp(x)=10.63	∑x^2p(x) = 63.01				<BR>\n" );
document.write( "							6^2=36									<BR>\n" );
document.write( "							91-4.472^2									 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825249 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825249\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "Hey, &nbsp;I looked at your post, &nbsp;and I see that parts &nbsp;(ii) &nbsp;and &nbsp;(iii) &nbsp;are solved incorrectly.\r<BR>\n" );
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document.write( "I think that you don't know relevant theory.\r<BR>\n" );
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document.write( "From the other side, &nbsp;I see your intention to do the job on your own, &nbsp;which I like very much.\r<BR>\n" );
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document.write( "So, &nbsp;my advise to you is to read a lesson\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Rolling-a-pair-of-fair-dice.lesson>Rolling a pair of fair dice</A> \r<BR>\n" );
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document.write( "in this site. &nbsp;You will find there many other similar solved problems.\r<BR>\n" );
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document.write( "After reading it, &nbsp;you will be able to solve the mentioned parts in a correct way, &nbsp;I believe.\r<BR>\n" );
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document.write( "When you redo and complete the parts &nbsp;(ii) &nbsp;and &nbsp;(iii) &nbsp;on your own, &nbsp;you may re-post your solution to this forum &nbsp;(to me) &nbsp;for checking.\r<BR>\n" );
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document.write( "David, &nbsp;&nbsp;I got your comment.\r<BR>\n" );
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document.write( "Your error in parts &nbsp;(ii) &nbsp;and &nbsp;(iii) &nbsp;is that you consider &nbsp;X &nbsp;as a variable for single separate throw,  \r<BR>\n" );
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document.write( "while the problem &nbsp;DEFINES &nbsp;&nbsp;X &nbsp;&nbsp;as the sum of values, &nbsp;when a pair of dice is thrown.\r<BR>\n" );
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document.write( "So, &nbsp;do not argue with me . . . // &nbsp;&nbsp;If your desire to argue with me prevails your desire to learn, &nbsp;then you are not my customer . . . \r<BR>\n" );
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document.write( "You better &nbsp;READ &nbsp;the lesson which &nbsp;I &nbsp;recommended you.\r<BR>\n" );
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document.write( "It is written &nbsp;SPECIALLY &nbsp;for those individuals who care about developing their  mind, &nbsp;their skills and their knowledge.\r<BR>\n" );
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document.write( "I will be glad to contact with you later, &nbsp;when I see your progress.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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