A rising density and a decreasing measurement scale
A rising density and a decreasing measurement scale
IB Year 6 | Grade 12
TGM Original
A continuous random variable X has probability density f(x)=2x for 0 <= x 1, and f(x)=0 otherwise. A measurement is reported as Y=10-6X. - Find the median and the mode of X. - Find E(X) and Var(X). - Find E(Y) and the standard deviation of Y. - Find P(Y 7), explaining the effect of the negative coefficient.
Solution:
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Answer:(a) median \(1/\sqrt2\), mode \(1\); (b) \(E(X)=2/3\), variance \(1/18\); (c) \(E(Y)=6\), standard deviation \(\sqrt2\); (d) \(3/4\).
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