<transcript><audio_6> and variance covariance matrix sigma. When does this happen? When we have standard normal, multivariate normal. Also, each component of Z is a standard normal distributed independently from</transcript><transcript><audio_7> तो Z हमारा किसको follow कर रहा है? Multivariate Standard Normal Distribution</transcript><caption><image_8>The image is a slide from a presentation on the probability density function of multivariate Normal distribution. The slide has a blue background with white text. On the left side of the slide, there is a title that reads "Theorem 1: Multivariate Normal". Below the title, there are two bullet points that explain the concept of the problem. 

The first bullet point explains that the problem is a multivariate normal distribution, which is a mathematical equation that shows the relationship between the two variables. The equation is written in black text on a white background. The second bullet point states that the probability of the function is under the transformation, and that it is also written in red text.

There is also a logo on the slide that says "Data".</caption><transcript><audio_9> we have the probability density function of multivariate normal distribution, this is the probability density function of multivariate normal है, under the transformation, अब वो transformation जो हमें given है transformation, उस से हम इसको further</transcript> Normal with mean vector zero and variance covariate matrix sigma This happens when we have standard normal multivariate normal also each component of z is a standard normal distributor independently from each other i.e. z follows the multivariate normal distribution and each component of z follows  The univariate standard normal distribution So, who are we following? The multivariate standard normal distribution. We have the probability density function of multivariate normal distribution. This is the probability density function of multivariate normal under the transformation. Now the transformation that is given to us is the transformation.  From that we are solving this,
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