document.write( "Question 860623: Please help me solve this problem of probability.
\n" ); document.write( "We throw two fair dice. Let Random Variable that gives the outcome of i die, for i=1,2.\r
\n" ); document.write( "\n" ); document.write( "i) Define an appropriate space of probability that describes the above experiment.
\n" ); document.write( "ii) Find the probability and equation of distribution of X1.
\n" ); document.write( "iii) Find the probability of random variable Z=7-X1. What do you observe?
\n" ); document.write( "iv) Find the probability of random variable Z=X1+X2.
\n" ); document.write( "v) What is the the most probable value for the sum of the two dice?
\n" ); document.write( "vi) What is the average value of the sum of the two dice? \n" ); document.write( "
Algebra.Com's Answer #518560 by rothauserc(4718)\"\" \"About 
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i) possible outcomes when rolling 2 dice, for each pair (a, b) a = first die, b = second die
\n" ); document.write( "1 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
\n" ); document.write( "2 (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
\n" ); document.write( "3 (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
\n" ); document.write( "4 (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
\n" ); document.write( "5 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
\n" ); document.write( "6 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
\n" ); document.write( "ii) X1 is a fair dice and possible outcomes are 1, 2, 3, 4, 5, 6. The probability of rolling any one of them is 1/6 and note that the sum of all six probalities must add up to 1, that is, the summation for i = 1 to 6 of Pi = 1
\n" ); document.write( "iii) Z=7-X1
\n" ); document.write( "P(7-1) = P(6) = 1/6, similarly P(i) where i = 1, 2...,6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1
\n" ); document.write( "iv) this is a normal distribution for the sum X1 + X2, we list pairs of (sum, probability)
\n" ); document.write( "(2, 1/36), (3, 2/36), (4, 3/36), (5, 4/36), (6, 5/36), (7, 6/36), (8, 5/36), (9, 4/36), (10, 3/36), (11, 2/36), (12, 1/36)
\n" ); document.write( "v) from iv we can see that the probability of rolling a 7 is 6/36 = 1/6 which is the largest value
\n" ); document.write( "vi) the average or mean is 7, the graph of probabilities is a norm distribution with 7 in the middle (mean). \n" ); document.write( "
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