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NIELIT 2021 Dec Scientist B - Section B: 71

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Let the random variable $\text{X}$ has a mixed distributions with probability $\text{P(X = 0)} = \alpha,$ and the density function.

$f_{x}(x) = \left\{\begin{matrix} \beta x^{2} (1 – x), 0 < x < 1& \\ 0, \text{otherwise}& \end{matrix}\right.$

If the expectation of $\text{X}$ is $\alpha,$ then the value of $4 \alpha + \beta$ is equal to :

  1. $9/2$
  2. $6$
  3. $9$
  4. $5/2$
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