How to compute MAP estimate It is a binary class problem class1=0 and class2=1.  It is known that the
likelihood function follows a Normal distribution with different parameters for different class label. There is only one attribute. Now, parameters of normal distribution are mean and variance_squared. For example following is the dataset
    x | y
    ______
    1 | 0
    2 | 0 
    3 | 0
    4 | 1
    5 | 1

prior probabilities will be 
P(C1)= 3/5
P(C2)= 2/5

Similarly, mean and variance for both class labels will be calculated.
What I am confused about is how do we compute MAP since there are two parameters?
Correct me if I am wrong on this one :
MAP1= mean1*variance1*P(C1)
MAP2= mean2*variance2*P(C2)

 A: I don't think the formulation of the problem is particularly clear. You don't specify what the distribution of $Y$ is but let's assume it's Bernoulli. Then the $P(Y=1)=0.6$ and $P(Y=0)=0.4$ are the posterior values given the data, not the prior values.
From your description, it's sounds your data is modelled by a mixture of two normal distributions. That is, 
$$
P(X | Y=0) = N_1(\mu_1,\sigma_1^2) \text{  and  } P(X | Y=1) = N_1(\mu_2,\sigma_2^2).
$$
Let $\theta = (\mu_1,\sigma_1^2, \mu_2,\sigma_2^2)$ be a vector containing the parameters. Then the MAP estimate for $\theta$ is given by 
$$
\hat{\theta}^{MAP} = \mathrm{argmax}_{\theta} P(X,Y| \theta)P(\theta).
$$
Notice you also have to specifiy a prior for $\theta$ which you have not done, hence I am not sure you have done your MAP estimates correctly. For mixture of Gaussians, the conjugate prior is usually the Dirichlet distribution. In the generic case, performing a MAP estimate for mixture models is a little tricky directly and is usually done with the EM algorithm. 
