We now toss a balanced coin Y, and draw a random variable X in R d
Ask Expert

Be Prepared For The Toughest Questions

Practice Problems

We now toss a balanced coin Y, and draw a random variable X in R d

6. Gaussian Mixture

Let µ0, µ1 ∈ R d , and let Σ0, Σ1 be two d × d positive definite matrices (i.e. symmetric with positive eigenvalues).

We now introduce the two following pdf over R d :


These pdf correspond to the multivariate Gaussian distribution of mean µ0 and covariance Σ0, denoted Nd(µ0, Σ0), and the multivariate Gaussian distribution of mean µ1 and covariance Σ1, denoted Nd(µ1, Σ1).

We now toss a balanced coin Y, and draw a random variable X in R d , following this process : if the coin lands on tails (Y = 0) we draw X rom Nd(µ0, Σ0), and if the coin lands on heads (Y = 1) we draw X from Nd(µ1, Σ1).

(a) Calculate P(Y = 0|X = x), the probability that the coin landed on tails given X = x ∈ R d , as a function of µ0, µ1, Σ0, Σ1, and x. Show all the steps of the derivation.

 

Hint
Statistics"The multivariate normal distribution, also known as the multivariate Gaussian distribution or joint normal distribution, is an extension of the one-dimensional (univariate) normal distribution to more dimensions in probability theory and statistics. Basic Methods for Generating a Random Variable Sources of physical matter Resampling based on empirical data. Pseudo-ra...

Know the process

Students succeed in their courses by connecting and communicating with
an expert until they receive help on their questions

1
img

Submit Question

Post project within your desired price and deadline.

2
img

Tutor Is Assigned

A quality expert with the ability to solve your project will be assigned.

3
img

Receive Help

Check order history for updates. An email as a notification will be sent.

img
Unable to find what you’re looking for?

Consult our trusted tutors.

Developed by Versioning Solutions.