A fair blue die has faces numbered 1, 1, 3, 3 and 5 - Edexcel - A-Level Maths Statistics - Question 6 - 2013 - Paper 1
Question 6
A fair blue die has faces numbered 1, 1, 3, 3 and 5. The random variable B represents the score when the blue die is rolled.
(a) Write down the probability distribu... show full transcript
Worked Solution & Example Answer:A fair blue die has faces numbered 1, 1, 3, 3 and 5 - Edexcel - A-Level Maths Statistics - Question 6 - 2013 - Paper 1
Step 1
Write down the probability distribution for B.
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Answer
The probability distribution for B, representing the score when the blue die is rolled, is as follows:
b
1
3
5
P(B = b)
2/5
2/5
1/5
Step 2
State the name of this probability distribution.
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Answer
This distribution is named a Discrete Uniform Distribution.
Step 3
Write down the value of E(B).
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Answer
The expected value E(B) can be calculated as:
E(B) = rac{1}{5}(1 + 1 + 3 + 3 + 5) = rac{13}{5} = 2.6
Step 4
Find E(R).
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Answer
To find E(R), we use the formula:
E(R) = rac{2}{3} imes 2 + rac{1}{6} imes 4 + rac{1}{6} imes 6 = rac{4}{3} + rac{2}{6} + 1 = rac{4}{3} + rac{1}{3} + rac{3}{3} = rac{8}{3}
Step 5
Find Var(R).
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Answer
To find Var(R), we first compute E(R²):
E(R²) = rac{2}{3}(2^2) + rac{1}{6}(4^2) + rac{1}{6}(6^2) = rac{2}{3}(4) + rac{1}{6}(16) + rac{1}{6}(36) = rac{8}{3} + rac{16}{6} + rac{36}{6}
