Question

A pixel in a particular image has a random brightness, X.The distribution of X depends on
whether the pixel belongs to an object (O) of interest or the background (B).If it belongs to
the object,then X has a Laplace distribution,
fX(x|O)=λ
2
exp(−λ|x|), −∞ < x < ∞,
where λ=0.2.If the pixel belongs to the background, then X is uniformly distributed
between -10 and 10.
Consider the problem of classifying a pixel based on an observation of its brightness, X = x.
(a)Find the ML rule for all values of x and illustrate the decision regions on a number line.
(b)Find the probability of error