Q20Comprehension3 Marks3 Dec 2024PassageBased on the above data, answer the given subquestions. Let X1,X2,…,XnX_1,X_2,\ldots,X_nX1,X2,…,Xn be i.i.d. Exp(1/3)\mathrm{Exp}(1/3)Exp(1/3) and Xˉ=X1+X2+⋯+Xnn\bar{X}=\frac{X_1+X_2+\cdots+X_n}{n}Xˉ=nX1+X2+⋯+Xn.Which of the following inequalities are true with respect to Chebyshev inequality?AP(∣Xˉ−3∣≥0.25)≤144nP(|\bar{X}-3|\ge0.25)\le \frac{144}{n}P(∣Xˉ−3∣≥0.25)≤n144BP(∣Xˉ−3∣≥0.6)≤1−111nP(|\bar{X}-3|\ge0.6)\le 1-\frac{111}{n}P(∣Xˉ−3∣≥0.6)≤1−n111CP(∣Xˉ−3∣≤0.5)≥1−36nP(|\bar{X}-3|\le0.5)\ge 1-\frac{36}{n}P(∣Xˉ−3∣≤0.5)≥1−n36DP(∣Xˉ−3∣≤0.25)≥36nP(|\bar{X}-3|\le0.25)\ge \frac{36}{n}P(∣Xˉ−3∣≤0.25)≥n36
