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2 dice are thrown. Suppose a random variable X is assigned a value 2 k , if the sum on the dice is equal to k , then the expected value of X is

Options

  1. A10
  2. B12
  3. C14
  4. D50 9

Correct answer

C. 14

Step-by-step solution

k 2 3 4 5 6 7 8 9 10 11 12 P k 1 36 2 36 3 36 4 36 5 36 6 36 5 36 4 36 3 36 2 36 1 36 k = sum on dice Expected value = 1 36 × 4 + 2 36 × 6 + 3 36 × 8 + 4 36 × 10 + 5 36 × 12 + 6 36 × 14 + 5 36 × 16 + 4 36 × 1 8 + 3 36 × 20 + 2 36 × 22 + 1 36 × 2 4 = 504 36 = 1 4

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