Suppose that the error in the reaction temperature ℃ , for a controlled laboratory experiment is a continuous r.v. X having the probability density function is: f(x)={( (cx^2)⁄3 -1 <X<2 0 otherwise)┤ Find P(0≤X<1)
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Mathematics
Since f(x) is a probability density function, then:
need an explanation for this answer? contact us directly to get an explanation for this answer∫_(-∞)^∞〖f(x)dx=〗 1
∴1=c/3 ∫_(-1)^2〖x^2 dx=c/3〗 [1/3 x^3 ]_(-1)^2
=c/9 [8+1]=c→c=1
P(0≤X<1)=1/3 ∫_0^1x^2 dx=1/3 [1/3 x^3 ]_0^1=1/9