<p>A random variable $X$ has the probability distribution given in the following table:</p>
<table><thead><tr><th>$x$</th><th>$2$</th><th>$3$</th><th>$4$</th><th>$5$</th></tr></thead><tbody><tr><td>${\mathbb{P}(X = x)}$</td><td>$p$</td><td>${\frac{2}{10}}$</td><td>${\frac{3}{10}}$</td><td>$q$</td></tr></tbody></table>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Given that $\mathrm{E}\left( X \right)=4$, find $p$ and $q$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Show that $\mathrm{Var}\left( X \right)=1$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find $\mathrm{E}\left( \left| X-4 \right| \right)$.</span></div></li><li><div class="list-item-paragraph">Ten independent observations of $X$ are taken. Find the probability that the value of $3$ is obtained at most $3$ times.</div></li></ol>

A random variable $X$ has the probability distribution given in the following table:

Given that $\mathrm{E}\left( X \right)=4$, find $p$ and $q$.

Show that $\mathrm{Var}\left( X \right)=1$.

Find $\mathrm{E}\left( \left| X-4 \right| \right)$.

Ten independent observations of $X$ are taken. Find the probability that the value of $3$ is obtained at most $3$ times.

N2001 P2 Q6

N2001 P2 Q6

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