document.write( "Question 1197519: q1)
\n" ); document.write( "A) random variable X is defined as the larger of the scores obtained in two throws of a fair six-sided die.Find the distribution of the random variable X.
\n" ); document.write( "(b)A random variable Y is defined as the highest score obtained in k throws of a fair six-sided die.Determine the probability mass function of Y .\r
\n" ); document.write( "\n" ); document.write( "q2)
\n" ); document.write( ".A white die and a red die are thrown at the same time and the difference W−R is observed ,where R is the number on top of the red die and W is that on top of the white one .Find the probability mass function of this difference W−R.\r
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Algebra.Com's Answer #830829 by math_tutor2020(3835) $\"\"$ $\"About$

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\n" ); document.write( "Question 1, Part (a)\r
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\n" ); document.write( "\n" ); document.write( "This is one way to write out the table of possible outcomes.
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	1	2	3	4	5	6
1	1	2	3	4	5	6
2	2	2	3	4	5	6
3	3	3	3	4	5	6
4	4	4	4	4	5	6
5	5	5	5	5	5	6
6	6	6	6	6	6	6

Example: We roll a 6 on the blue die and a 1 on the red die. The result is 6 since it's the larger of the two outcomes (top right corner of the table).\r
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\n" ); document.write( "\n" ); document.write( "The possible outcomes are: 1,2,3,4,5,6
\n" ); document.write( "Let X be those possible outcomes.\r
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\n" ); document.write( "\n" ); document.write( "Here's the frequency chart
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X	Frequency
1	1
2	3
3	5
4	7
5	9
6	11

\n" ); document.write( "We'll divide each frequency over 36 since there are 6*6 = 36 outcomes.\r
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\n" ); document.write( "\n" ); document.write( "Therefore, we have this probability mass function (PMF).
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X	P(X)
1	1/36
2	3/36
3	5/36
4	7/36
5	9/36
6	11/36

I decided not to reduce the fractions so that each could keep the consistent denominator of 36. \r
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\n" ); document.write( "\n" ); document.write( "If you want to reduce the fractions, then,
\n" ); document.write( "3/36 = 1/12
\n" ); document.write( "9/36 = 1/4\r
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\n" ); document.write( "\n" ); document.write( "================================================
\n" ); document.write( "Question 1, Part (b)\r
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\n" ); document.write( "\n" ); document.write( "Right now I'm blanking on how to do this, so I'll come back to this later. Or I'll let another tutor step in. Sorry for the trouble.\r
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\n" ); document.write( "\n" ); document.write( "The slight good news is that I managed to find the PMF tables for k = 3 through k = 5 using computer software. But I wasn't able to find a generalized case for any positive integer k value.\r
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\n" ); document.write( "\n" ); document.write( "PMF for k = 3
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X	P(X)
1	1/216
2	7/216
3	19/216
4	37/216
5	61/216
6	91/216

\r
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\n" ); document.write( "\n" ); document.write( "PMF for k = 4
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X	P(X)
1	1/1296
2	15/1296
3	65/1296
4	175/1296
5	369/1296
6	671/1296

\r
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\n" ); document.write( "\n" ); document.write( "PMF for k = 5
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X	P(X)
1	1/7776
2	31/7776
3	211/7776
4	781/7776
5	2101/7776
6	4651/7776

\r
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\n" ); document.write( "\n" ); document.write( "================================================
\n" ); document.write( "Question 2\r
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\n" ); document.write( "\n" ); document.write( "We'll use the template from the table in question 1, part (a).\r
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\n" ); document.write( "\n" ); document.write( "Instead of white, I'll use blue.
\n" ); document.write( "We subtract the values in the format B - R
\n" ); document.write( "B = blue
\n" ); document.write( "R = red
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	1	2	3	4	5	6
1	0	1	2	3	4	5
2	-1	0	1	2	3	4
3	-2	-1	0	1	2	3
4	-3	-2	-1	0	1	2
5	-4	-3	-2	-1	0	1
6	-5	-4	-3	-2	-1	0

\n" ); document.write( "For example, if we roll a 6 on the blue die and a 1 on the red die, then B-R = 6-1 = 5 which is in the top right corner of the table.\r
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\n" ); document.write( "\n" ); document.write( "The outcomes range from -5 to +5 inclusive of the endpoints.
\n" ); document.write( "Let X be the result of each difference\r
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X	Frequency
-5	1
-4	2
-3	3
-2	4
-1	5
0	6
1	5
2	4
3	3
4	2
5	1

\n" ); document.write( "Then we divide each frequency over 36 to form the PMF.
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X	P(X)
-5	1/36
-4	2/36
-3	3/36
-2	4/36
-1	5/36
0	6/36
1	5/36
2	4/36
3	3/36
4	2/36
5	1/36

\n" ); document.write( "Once again, I chose not to reduce the fractions to keep the same denominator (36).
\n" ); document.write( "If you want to reduce the fractions, then,
\n" ); document.write( "2/36 = 1/18
\n" ); document.write( "3/36 = 1/12
\n" ); document.write( "4/36 = 1/9
\n" ); document.write( "6/36 = 1/6
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