From the given Probability Mass Function of Y, the following Table is formed:
| y | p | yp | y2 p |
| 0 | 0.5 | 0 | 0 |
| 1 | 0.4 | 0.4 | 0.4 |
| 2 | 0.1 | 0.2 | 0.4 |
| Total = | 1.0 | 0.6 | 0.8 |


Variance of Y is given by:

So,
Answer is:
0.44
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