<p>Given that&nbsp;$X\sim N(10,12)$ and $Y\sim N(5,8)$. Find the normal distribution of</p>
<ol class="i-list"><li><div class="list-item-paragraph">$4X+2Y$ </div></li><li><div class="list-item-paragraph">$3X-4Y$ </div></li><li><div class="list-item-paragraph">${{X}_{1}}+{{X}_{2}}+{{X}_{3}}-{{Y}_{1}}-{{Y}_{2}}-{{Y}_{3}}-{{Y}_{4}}$ </div></li></ol>

Given that $X\sim N(10,12)$ and $Y\sim N(5,8)$. Find the normal distribution of

${{X}_{1}}+{{X}_{2}}+{{X}_{3}}-{{Y}_{1}}-{{Y}_{2}}-{{Y}_{3}}-{{Y}_{4}}$ 

Normal Distribution

International Baccalaureate Higher Level Mathematics

Linear Combinations of Normal Random Variables

Linear Combinations of Normal Random Variables