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VICMath MethodsQuick questions

Unit 4

Quick questions on Continuous random variables: VCE Math Methods Unit 4

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is worked variance?
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For the pdf f(x)=x8f(x) = \frac{x}{8} on [0,4][0, 4] (worked above), E(X)=83E(X) = \frac{8}{3}, E(X2)=8E(X^2) = 8, Var(X)=89\text{Var}(X) = \frac{8}{9}, σ=223\sigma = \frac{2 \sqrt{2}}{3}.
What is wrong formula for variance?
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Var(X)=E(X2)−[E(X)]2\text{Var}(X) = E(X^2) - [E(X)]^2, not E(X2)−E(X)E(X^2) - E(X) or E(X)2−E(X2)E(X)^2 - E(X^2). The square applies to the mean.
What is q1?
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A pdf is f(x)=kxf(x) = kx on [0,4][0, 4], zero elsewhere. Find kk. [2 marks]
What is q2?
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For f(x)=18xf(x) = \frac{1}{8}x on [0,4][0, 4], find P(1≤X≤3)P(1 \le X \le 3). [2 marks]
What is q3?
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For f(x)=18xf(x) = \frac{1}{8}x on [0,4][0, 4], find the median mm. [3 marks]

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