Problem 1: Let $Y_{1}, Y_{2}, \ldots$ be a sequence of random variables such that $$ P\left(Y_{n}=\frac{1}{n} ight)=1-\frac{1}{n^{2}} \text { and } P\left(Y_{n}=n ight)=\frac{1}{n^{2}} \text {. } $$ Does $Y_{n} $ converge in probability? Prove your claim. SP.AS. 1134