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A random variable y has a known probability distribution given by

y 2 4 6 8 10
P(y) 0.17 0.23 0.2 0.3 0.1

Then the expected value of y is

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  1. 7.67
  2. 6.88
  3. 5.86
  4. 4.89

Answer (Detailed Solution Below)

Option 3 : 5.86
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Detailed Solution

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Calculation

We know expected value of random variable

f(x) = ∑xipi

where I = 1, 2, 3,-----n

f(x) = P1x1 + P2x2 + P3x3 + P4x4 + P5x5

⇒ f(x) = 0.17 × 2 + 0.23 × 4 + 0.2 × 6 + 0.3 × 8 + 0.1 × 10

∴ f(x) = 5.86

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