Hi I am solving one problem based Bayes' formula. I need to calculate the normal distribution of P(x|y). The following data is given.
P(x | y = 0) = N(x1,0,1) and P(x | y = 1) = N(x2,0,16)
where N stands for density of Normal Distribution where mean is 0 and variances are 1 and 16 respectively. P(y=0) = P(y=1) = 0.5.
I have calculated the normal distribution of P(x|y) as. P(x | y) = 0.5 * N(x1,0,1)+ 0.5 N(x2,0,16)
My approach is correct or not. Any help in this regard is appreciated.