A discrete random variable X has the probability distribution given as below:

(i) Find the value of k

(ii) Determine the mean of the distribution.

Given table—

(i) We know that , where pi ≥0

P₁+ P₂+ P₃+ P₄ = 1

k+ k²+2k²+ k = 1

3k² + 2k -1= 0

3k² + 3k- k- 1 = 0

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

Since, k≥ 0, we take

(ii)

= 0.5(k)+ 1(k²) + 1.5(2k²) + 2(k)

= 4k² + 2.5k