A discrete random variable `X` has the probability distribution given below: `X :\ 0. 5 \ \ 1\ \ 1.5 \ \ 2` `P(X):\ \ k \ \ k^2 \ \ 2k^2 \ \ k` i. Find the value of `k`. ii. Determine the mean of the distribution.

Answer

when `k=1/3` the mean is `1.28`

and when `k=-1` the mean is `1.5`

Explanation

We know that in Probability distribution sum of all Probabilities is equal to `1`


`Sigma p_i=1`


`rArr k+k^2+2k^2+k=1`


`rArr 3k^2+2k=1`


`rArr 3k^2+2k-1=0`


`rArr 3k^2+3k-k-1=0`


`rArr 3k(k+1)-1(k+1)=0`


`rArr (3k-1)(k+1)=0`


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