Q#1 A continuous random variable X has the density function f(x)=x for 0<x<1 2-x for 1_<x<2 0 elsewhere a. Show that P(0<X<2)=1 b. Find P(X<1.2).
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Originally Posted by nisoo-1 Q#1 A continuous random variable X has the density function f(x)=x for 0<x<1 2-x for 1_<x<2 0 elsewhere a. Show that P(0<X<2)=1 $\displaystyle P(0<x<2) = \int_0^2 f(x) ~dx = \int_0^1 x ~dx + \int_1^2 (2-x)~dx= 1/2 + 1/2=1 $ RonL
Originally Posted by nisoo-1 Q#1 A continuous random variable X has the density function f(x)=x for 0<x<1 2-x for 1_<x<2 0 elsewhere b. Find P(X<1.2). $\displaystyle P(x<1.2) = \int_0^{1.2} f(x) ~dx = \int_0^1 x ~dx + \int_1^{1.2} (2-x)~dx = 1/2 + \left[ 2x-x^2/2\right]_1^{1.2}$ RonL
Calculus may be a bit much for this problem. If you are supposed to use it, fine, but please keep in mind there may be other ways of going about things. In this case, if you know a little about right triangles it is just as straight-forward.
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