Let Zn BE X2(n) (Chi-square) and let Wn = Zn/n2. Find the limiting distribution of Wn using the Weak Law of Large Numbers
Let Zn BE X2(n) (Chi-square) and let Wn = Zn/n2. Find the limiting distribution of Wn...
Let Yn be a chi square random variable with n degrees of freedom, and let Xn = Yn / n2. Find the limiting distribution of Xn.
5. Let Xn ~ χ2 (n), n-1, 2, . . . . Find the limiting distribution of X,1/n2.
Let X1, X2, .. , Xn be a random sample of size n from a geometric distribution with pmf =0.75 . 0.25z-1, f(x) X-1.2.3. ) Let Zn 3 n n-2ућ. Find Mz, (t), the mgf of Žn. Then find the limiting mgf limn→oo MZm (t). What is the limiting distribution of Z,'? Let X1, X2, .. , Xn be a random sample of size n from a geometric distribution with pmf =0.75 . 0.25z-1, f(x) X-1.2.3. ) Let Zn 3...
2) Let X,..X, be ii.d. N(O, 1) random variables. Define U- Find the limiting distribution of Zn (Hint: Recall that if X and Y are independent N(0, 1) random variables, then has a Cauchy distribution 2) Let X,..X, be ii.d. N(O, 1) random variables. Define U- Find the limiting distribution of Zn (Hint: Recall that if X and Y are independent N(0, 1) random variables, then has a Cauchy distribution
2. The chi-square distribution plays a significant role in performing inference on the as- sociation between categorical random variables (e.g., car injury severity and seat belt usage). If Z ~ N(0,1), then W = Z2 ~ xỉ – that is, W has a chi-square distribution with 1 degree of freedom. Furthermore if Z1, Z2, ..., Zn N(0,1), then W = Z+Z2+...+22 has a chi-square distribution with n degrees of freedom. Here are some helpful facts. Let t > 0 •...
Please proof X^2(n) using the standard normal distribution Chi-square distribution
uiing lavieu valués of the chi-square distribution The distance in feet by which a parachutist misses a target is D = Vxi + x3, where X and X2 are independent with X~N(0, 25). Find P[D < 12.25 feet].
Find the following chi-square distribution values from Table 11.1 (to 3 decimals). a. X2 os with öf- 5 b. X 2 025 with df- 15 c. χ 2 .975 with d-20 d, χ 2 .01 with df-10 e, χ 2 .95 with df-18
Let X1, X2, ..., Xn be a random sample with probability density function a) Is ˜θ unbiased for θ? Explain. b) Is ˜θ consistent for θ? Explain. c) Find the limiting distribution of √ n( ˜θ − θ). need only C,D, and E Let X1, X2, Xn be random sample with probability density function 4. a f(x:0) 0 for 0 〈 x a) Find the expected value of X b) Find the method of moments estimator θ e) Is θ...
Solve b 3.6.14. Let Xi, X2, and Xs be three independent chi-square variables with rı, r2, and T3 degrees of freedom, respectively. (a) Show that Yı = X1/X2 and ½ = X1 + X2 are independent and that ½ is x 2) (b) Deduce that and KJr2 (X1+X2)/(n+r2) are independent F-variables. 3.6.14. Let Xi, X2, and Xs be three independent chi-square variables with rı, r2, and T3 degrees of freedom, respectively. (a) Show that Yı = X1/X2 and ½ =...