An ecologist wishes to mark off circular sampling regions of nearly 10 m in diameter. However the actual diameter of the marked region varies and is a random variable. Let X= actual diameter of a sampled region. The pdf of X is given as f(x)= k[1-(10-x)^3]; 9sxs 12 Hint: (a-b)^3= a^3 - 3*a^2*b+ 3*a*b^2 - b^3 { 0; otherwise Find the value of K for which the above pdf f(x) is valid.

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An ecologist wishes to mark off circular sampling regions of nearly 10 m in diameter. However the actual diameter of the
marked region varies and is a random variable. Let X= actual diameter of a sampled region.
The pdf of X is given as
|f(x)=
k[1-(10-x)^3];
9<x< 12
Hint: (a-b)^3= a^3 - 3*a^2*b+ 3*a*b^2 - b^3
{
0;
otherwise
Find the value of K for which the above pdf f(x) is valid.
Transcribed Image Text:An ecologist wishes to mark off circular sampling regions of nearly 10 m in diameter. However the actual diameter of the marked region varies and is a random variable. Let X= actual diameter of a sampled region. The pdf of X is given as |f(x)= k[1-(10-x)^3]; 9<x< 12 Hint: (a-b)^3= a^3 - 3*a^2*b+ 3*a*b^2 - b^3 { 0; otherwise Find the value of K for which the above pdf f(x) is valid.
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