Question: Problem 4: Suppose that $P(Y=1 )=P(Y=-1)=1 / 2$. Define $$ Y_{n}=left{begin{array}{11} Y & text { with probability } 1-frac{1}{n} e^{n} & text { with probability

$Problem 4: Suppose that $P(Y=1 )=P(Y=-1)=1 / 2$. Define $$ Y_{n}=\left\{\begin{array}{11}$

Problem 4: Suppose that $P(Y=1 )=P(Y=-1)=1 / 2$. Define $$ Y_{n}=\left\{\begin{array}{11} Y & \text { with probability } 1-\frac{1}{n} e^{n} & \text { with probability } \frac{1}{n} \end{array} ight. $$ Does $Y_{n}$ converge to $y$ in probability? Does $Y_{n}$ converge to $y$ in distribution? Prove your claims. SP.AS. 1138

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