(a) Give an example of a random variable Y such that E(Y)=0 and E Y^2<∞, E|Y^2+δ|=∞, for all δ

(a) Give an example of a random variable Y such that E(Y)=0...

(a) Give an example of a random variable $Y$ such that $E(Y)=0$ and $$ E Y^2<\infty, \quad E\left|Y^{2+\delta}\right|=\infty, $$ for all $\delta>0$. (This means finding a probability density.) (b) Suppose $\left\{Y_n, n \geq 1\right\}$ are iid with $E Y_1=0$, and $E Y_1^2=\sigma^2<\infty$. Suppose the common distribution is the distribution found in (a). Show that Lindeberg's condition holds but Liapunov's condition fails.

(a) Give an example of a random variable $Y$ such that $E(Y)=0$ and

$$
E Y^2<\infty, \quad E\left|Y^{2+\delta}\right|=\infty,
$$

for all $\delta>0$. (This means finding a probability density.)
(b) Suppose $\left\{Y_n, n \geq 1\right\}$ are iid with $E Y_1=0$, and $E Y_1^2=\sigma^2<\infty$. Suppose the common distribution is the distribution found in (a). Show that Lindeberg's condition holds but Liapunov's condition fails.

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