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In: Statistics and Probability

A regular six-sided die and a regular eight-sided die are rolled to find the sum. Determine...

A regular six-sided die and a regular eight-sided die are rolled to find the sum. Determine the probability distribution for the sum of the two dice. Create a frequency histogram for the probability distribution and determine the expected sum of the two dice.

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Expert Solution

Solution:-

The probability distribution for the sum of the two dice.

Sum(x) Frequency P(x)
2 1 0.020833
3 2 0.041667
4 3 0.0625
5 4 0.083333
6 5 0.104167
7 6 0.125
8 6 0.125
9 6 0.125
10 5 0.104167
11 4 0.083333
12 3 0.0625
13 2 0.041667
14 1 0.020833
Sum 48 1

The frequency histogram for the probability distribution is

The expected sum of two dices is 8

Sum(x) Frequency P(x) x*P(x)
2 1 0.020833 0.041667
3 2 0.041667 0.125
4 3 0.0625 0.25
5 4 0.083333 0.416667
6 5 0.104167 0.625
7 6 0.125 0.875
8 6 0.125 1
9 6 0.125 1.125
10 5 0.104167 1.041667
11 4 0.083333 0.916667
12 3 0.0625 0.75
13 2 0.041667 0.541667
14 1 0.020833 0.291667
Sum 48 1 8

E(x) = x*P(x)

E(x) = 8

orchestra answered 1 year ago
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