If a random variable (X ) takes the values (x₁, x₂, x₃, , x₁₀₀ ) with probability (P (X=x_i )= ) (K i(i+1) ), then (200 K= )

Step-by-step solution

It is given that for random variable (X ) which can take values (x₁, x₂, x₃, . ., x₁₀₀ ) with probability (P (x=x_i )=K i(i+1) ) ( aligned & _ i=1 ¹⁰⁰ P (X=x_i )=1 K _ i=1 ¹⁰⁰ i(i+1)=1 & K _ i=1 ¹⁰⁰ (i^2+i )=1 & K [ 100(100+1)(200+1) 6 + 100(100+1) 2 ]=1 & K 100 101 6 [201+3]=1 & K= 6 100 101 204 [201+3]=1 & 200 K=200 6 100 101 204 = 1 101 17 = 1 1717 aligned ) Hence, option (b) is correct.