# Independent random variables X_{1} and X_{2} are combined according to the formula L = 3*X_{1} + 2*X_{2}. If X_{1} and X_{2} both have a variance of 2.0, what is the variance of L?

Question
Random variables
Independent random variables $$\displaystyle{X}_{{{1}}}{\quad\text{and}\quad}{X}_{{{2}}}$$ are combined according to the formula $$\displaystyle{L}={3}\cdot{X}_{{{1}}}+{2}\cdot{X}_{{{2}}}$$.
If $$\displaystyle{X}_{{{1}}}{\quad\text{and}\quad}{X}_{{{2}}}$$ both have a variance of 2.0, what is the variance of L?

2020-11-23
Step 1
$$\displaystyle{X}_{{{1}}}{\quad\text{and}\quad}{X}_{{{2}}}$$ are independent random variables.
$$\displaystyle{V}{\left({X}_{{{1}}}\right)}={V}{\left({X}_{{{2}}}\right)}={2}$$
$$\displaystyle{C}{O}{V}{\left({X}_{{{1}}},{X}_{{{2}}}\right)}={0},{a}{s}{X}_{{{1}}}{\quad\text{and}\quad}{X}_{{{2}}}$$ are independent random variables.
$$\displaystyle{V}{\left({L}\right)}={V}{\left({3}{X}_{{{1}}}+{2}{X}_{{{2}}}\right)}={9}{V}{\left({X}_{{{1}}}\right)}+{4}{V}{\left({X}_{{{2}}}\right)}+{12}{C}{O}{V}{\left({X}_{{{1}}},{X}_{{{2}}}\right)}$$
$$\displaystyle={9}\cdot{2}+{3}\cdot{2}$$
$$\displaystyle={13}\cdot{2}={26}$$
$$\displaystyle{V}{\left({L}\right)}={26}$$

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White - 67
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Let's compare the percentage of unarmed shot for each race.
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f) What percent are Hispanic and Unarmed?
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g) What percent of blacks shot and killed by police were unarmed?
h) What percent of whites shot and killed by police were unarmed?
i) What percent of Hispanics shot and killed by police were unarmed?
You can see by the answers to part g and h, that the percentage of blacks that were unarmed and killed by police is approximately twice that of whites that were unarmed and killed by police.
j) Why do you believe this is happening?
Do a search on the internet for reasons why blacks are more likely to be killed by police. Read a few articles on the topic. Write your response using the articles as references. Give the websites used in your response. Your answer should be several sentences long with at least one website listed. This part of this problem will be graded after the due date.
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