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JEE Math Practice Question

If the mean of the following probability distribution of a radam variable $$\mathrm{X}$$ : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-baqh{text-align:center;vertical-align:top} $$\mathrm{X}$$ 0 2 4 6 8 $$\mathrm{P(X)}$$ $$a$$ $$2a$$ $$a+b$$ $$2b$$ $$3b$$ is $$\frac{46}{9}$$, then the variance of the distribution is

  1. A.$$\frac{581}{81}$$
  2. B.$$\frac{566}{81}$$
  3. C.$$\frac{151}{27}$$
  4. D.$$\frac{173}{27}$$

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