Q16Comprehension2 Marks3 Dec 2024PassageBased on the above data, answer the given subquestions. Let X∼Uniform[0,5]X\sim \mathrm{Uniform}[0,5]X∼Uniform[0,5] and g(x)=(x−2)2g(x)=(x-2)^2g(x)=(x−2)2. Define a new random variable Y=g(X)Y=g(X)Y=g(X).Find the CDF of YYY.AFY(y)=2y5F_Y(y)=\frac{2\sqrt{y}}{5}FY(y)=52y, 0≤y≤90\le y\le 90≤y≤9BFY(y)=y5F_Y(y)=\frac{\sqrt{y}}{5}FY(y)=5y, 0≤y≤90\le y\le 90≤y≤9CFY(y)=2y5F_Y(y)=\frac{2\sqrt{y}}{5}FY(y)=52y, 0≤y≤40\le y\le 40≤y≤4; 2+y5\frac{2+\sqrt{y}}{5}52+y, 4<y≤94<y\le 94<y≤9DFY(y)=3y10F_Y(y)=\frac{3\sqrt{y}}{10}FY(y)=103y, 0≤y≤40\le y\le 40≤y≤4; 2y−15\frac{2\sqrt{y}-1}{5}52y−1, 4<y≤94<y\le 94<y≤9
