<caption><image_0>The image is a slide from a presentation on the concept of Multivariate Normal. The slide has a blue background with white text. On the right side of the slide, there is a logo of a person's hand holding a magnifying glass with the word "DATA" written on it. Below the logo, there are two bullet points that explain the concept.

The first bullet point reads "Theorem 1: Multivariate normal" and the second bullet point states that if g is N, where, it is a positive definite symmetric matrix there. A distributed as multivariate normal with mean vector 0 and variance covariance matrix is also, each component of g is standard normal, distributed independent from each other.</caption><transcript><audio_1> theorem 1 multivariate normal का अब theorem 1 basically हमारे पास क्या है हमने इसे check करना है if x is a multivariate normal with parameter mean mu and variance sigma variance covariance matrix sigma</transcript><transcript><audio_2> positive definite symmetric matrix, then Z, अब ये Z हमारे पास क्या, which is equals to, variance covariance matrix, minus 1x,</transcript><transcript><audio_3> x minus mu transpose sigma inverse x minus mu अब यहां हमने क्या किया है कि half इस site</transcript><transcript><audio_4> information हम basically क्यों कर रहे हैं क्योंकि आप देखो जब हमने variable को transform करना है तो उसका क्या result आता है जैसे rupees को हम dollar में convert करते हैं transformed कर रहे हैं तो इस type पे अगर हमारे किसी variable को original</transcript><transcript><audio_5> तो फिर क्या effect आ रहा है multivariate normal में हम उससे check करते हैं x की distribution हमारे पास multivariate normal है ठीक है तो जो</transcript> In this lecture we are checking theorem one of multivariate normal now theorem one basically what we have is we have to check that if x is a multivariate normal with parameter mean m and variance sigma variance covariance matrix sigma where sigma is a positive definite  Symmetric matrix given What's in the PDF? Pass one minus m transposing ma inverse Why are we doing transformation in new variable basically because you see when we have to transform the variable then what is its result like we convert rupees into dollars, when we are transforming then in this type if any of our variables is changed from the original variable.  If we start doing transformation then what effect is coming? We check it in multivariate normal. The distribution of
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