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STEP II 2007 question 14 solutionTSR Wiki > Study Help > Subjects and Revision > Mathematics > STEP > STEP II 2007 question 14 solution (i) The sketch should be straightforward: a curve (in the shape of (ii) Noticing the less than [B]or equal to[/B] signs, we can say that
Solving these simultaneously yields:
Now the total area under the pdf must be equal to 1, and hence Unparseable or potentially dangerous latex formula. Error 4: no dvi output from LaTeX. It is likely that your formula contains syntax errors or worse. (note the areas of two of the sections are simply rectangles and triangles and so integration is overkill)
\displaystyle \int^{4k}_1{\ln{x} \text{ d} x+k\ln{k}+k\ln{k}=1 Evaluating the integral and gathering like terms, we find
Now as
(iii) Using as estimate for Let us call the median Unparseable or potentially dangerous latex formula. Error 4: no dvi output from LaTeX. It is likely that your formula contains syntax errors or worse. by the definition of the median that:
\displaystyle \int^{e^{1/3}}_1{\ln{x}\text{ d} x+\frac13(\gamma-e^{1/3})=\frac13(2e^{1/3}-\gamma)+\frac13 e^{1/3}
Evaluating the integral and tidying up, we see
Solution by coffeym. |
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