The continuous r.v. X has the p.d.f: f(x)={( 1/2 x 0< X≤1 1/4(3-x) 1<X≤2 1/4 3<X≤4 0 otherwise)┤ Find: P(|X|<1.5)
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total answers (1)
total answers (1)
Mathematics
P(|X|<1.5)=P(-1.5<X<1.5)
need an explanation for this answer? contact us directly to get an explanation for this answer=∫_(-1.5)^1.5〖f(x)〗 dx=∫_(-1.5)^0〖f(x)〗 dx+∫_0^1〖f(x)〗 dx+∫_1^1.5〖f(x)〗 dx
= ∫_0^1 1/2 xdx+∫_1^1.5 1/4 (3-x)dx
=1/2 [1/2 x^2 ]_0^1+1/4 [3x-1/2 x^2 ]_1^1.5
=1/4+1/4 [3(3/2)-1/2 (3/2)^2-3+1/2]
=1/4 [1+(9/2)-9/8-3+1/2]=15/32