If `X` is a random variable with probability distribution as given below: `X=x_i :\ 0 \ \ 1 \ \ 2 \ \ 3` `P(X=x_i): k \ \ 3k \ \ 3k \ \ k` The value of `k` and its variance are (A) `1/8, 22/27` (B) `1/8, 23/27` (C) `1/8, 24/27` (D) `1/8,3/4`

Explanation

`sum_{{i}=-2}^{3} {p}_{{i}}=1 `


`{k}+3 {k}+3 {k}+{k}=1 `


`Rightarrow {k}=frac{1}{8}
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`
{E}[{X}]=sum_{{i}=0}^{3} {x}_{{i}} {p}_{{i}}=0 times {P}({X}=0)+1 times {P}({X}=1)+2 times {P}({X}=2)+3 times {P}({X}=3)
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