<p>The discrete random variable \(X\) has p.d.f. given by \(P(X=x) = qp^{x}\), where&nbsp;\(x = 0, 1, 2, \dots\)</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Express \(q\) in terms of \(p\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find \(\mathrm{E}(X)\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find \(\mathrm{E}(X(X-1))\) and determine \(\mathrm{E}(X^2)\), and hence&nbsp;\(\mathrm{Var}(X)\).</span></div></li></ol>

The discrete random variable \(X\) has p.d.f. given by \(P(X=x) = qp^{x}\), where \(x = 0, 1, 2, \dots\)

Find \(\mathrm{E}(X(X-1))\) and determine \(\mathrm{E}(X^2)\), and hence \(\mathrm{Var}(X)\).

Probability Distribution Table

Discrete Random Variables (DRV)

International Baccalaureate Higher Level Mathematics

Computation of variance using transformed variable

Computation of variance using transformed variable