If a random variable X has the following probability distribution, then its variance is nearly array |c|c|c|c|c|c|c|c| X =x: & -3 & -2 & -1 & 0 & 1 & 2 & 3 P ( X =x): & 0.05 & 0.1 & 2 ~K & 0 & 0.3 & ~K & 0.1 array

Step-by-step solution

array |c|c|c|c|c|c|c|c| X = x & -3 & -2 & -1 & 0 & 1 & 2 & 3 P ( X = x ) & 0.05 & 0.1 & 2 k & 0 & 0.3 & k & 0.1 array aligned & P ( X =x)=1 & 0.05+0.1+2 k+0+0.3+k+0.1=1 k=0.15 aligned array |c|c|c|c|c|c|c|c| X = x & -3 & -2 & -1 & 0 & 1 & 2 & 3 P ( X = x ) & 0.05 & 0.1 & 0.3 & 0 & 0.3 & 0.15 & 0.1 array aligned & Mean ( )=(-3)(0.05)+(-2)(0.1)+(-1)(0.3) & +(1)(0.3)+2(0.15)+3(0.1)=0.25 & Variance = _ i=1 ^7 (x_i- )^2 P (x_i ) & =0.528125+0.50625+0.46875+0+0.16875 & +0.459375+0.75625=2.8875 aligned