(i) We know that:
(ii) Now, the distribution becomes
![\[E({{X}^{2}})\text{ }=\text{ }1\text{ }\times \text{ 1/2 }+\text{ }4\text{ }\times \text{ }1/5\text{ }+\text{ }16\text{ }\times 3/25\text{ }+\text{ }36\text{ }\times 1/10\text{ }+\text{ }81\text{ }\times 1/25\text{ }+\text{ }225\text{ }\times \text{ }1/25\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c6a9935c821a646ecb7c294e7139c2d9_l3.png "Rendered by QuickLaTeX.com")
=
![\[1/2+\text{ }4/5\text{ }+\text{ }48/25\text{ }+\text{ }36/10\text{ }+\text{ }81/25\text{ }+\text{ }225/25\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f0efc6914a46f7e6cd90c192ebd91bfb_l3.png "Rendered by QuickLaTeX.com")
=
![\[0.5\text{ }+\text{ }0.8\text{ }+\text{ }1.92\text{ }+\text{ }3.6\text{ }+\text{ }3.24\text{ }+\text{ }9\text{ }=\text{ }19.06\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f69d40e4990c71efb489817f38dbad4f_l3.png "Rendered by QuickLaTeX.com")
Variance (X) =
![\[E({{X}^{2}})\text{ }\text{ }{{\left[ E\left( X \right) \right]}^{2}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6371cf62528a31edb8a4ca4e2538e0ab_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }19.06\text{ }\text{ }{{\left( 2.94 \right)}^{2}}~=\text{ }19.06\text{ }\text{ }8.64\text{ }=\text{ }10.42\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-bd58f583cba2e07be99e70210f608baa_l3.png "Rendered by QuickLaTeX.com")
The probability distribution of a discrete random variable X is given as under: Calculate: (i) The value of A if E(X) =
![\[2.94\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dc4a155e0dbba391251d3c9a51f46671_l3.png "Rendered by QuickLaTeX.com")
The probability distribution of a discrete random variable X is given as under: Calculate: (i) The value of A if E(X) =