Q10Single correct3 Marks6 Aug 2023Suppose X∼Bernoulli(0.4)X \sim \text{Bernoulli}(0.4)X∼Bernoulli(0.4) and Y∣X=x∼Uniform(x−1,x+1)Y\mid X=x \sim \text{Uniform}(x-1,x+1)Y∣X=x∼Uniform(x−1,x+1). Find the density of YYY.AfY(y)={1/3, −1≤y≤2; 0, otherwise}f_Y(y)=\{1/3,\ -1\le y\le 2;\ 0,\ \text{otherwise}\}fY(y)={1/3, −1≤y≤2; 0, otherwise}BfY(y)={0.3, −1≤y<0; 0.5, 0≤y<1; 0.2, 1≤y<2; 0, otherwise}f_Y(y)=\{0.3,\ -1\le y<0;\ 0.5,\ 0\le y<1;\ 0.2,\ 1\le y<2;\ 0,\ \text{otherwise}\}fY(y)={0.3, −1≤y<0; 0.5, 0≤y<1; 0.2, 1≤y<2; 0, otherwise}CfY(y)={0.2, −1≤y<0; 0.5, 0≤y<1; 0.8, 1≤y<2; 0, otherwise}f_Y(y)=\{0.2,\ -1\le y<0;\ 0.5,\ 0\le y<1;\ 0.8,\ 1\le y<2;\ 0,\ \text{otherwise}\}fY(y)={0.2, −1≤y<0; 0.5, 0≤y<1; 0.8, 1≤y<2; 0, otherwise}DfY(y)={0.5, −1<y<1; 0, otherwise}f_Y(y)=\{0.5,\ -1<y<1;\ 0,\ \text{otherwise}\}fY(y)={0.5, −1<y<1; 0, otherwise}
