Part A Let $a$ and $b$ be constants. Suppose that $X_{n} ightarrow^{p} a, Y_{n} ightarrow^{p} b$, and $Z_{n} ightarrow^{d} Z$ where $2$ is a random variable. Show that $$ X_{n}+Y_{n} Z_{n} ightarrow^{d} a+b Z $$ using the properties we learned in class. Part B Prove or disprove (i.e. provide a counterexample, the following: If $X_{n} ightarrow^{d} X$ and $Y_{n} ightarrow"{d} Y$, then $X_{n}+Y_{n} ightarrow^{d}$ $X+Y$. SP.PC.087