<transcript><audio_18> But this is the density function of multivariate normal distribution with mean vector zero and variance covariance metric identity metric.</transcript><transcript><audio_19> is the multivariate normal distribution with mean vector mu and</transcript><transcript><audio_20> mean vector 0 and variance covariance matrix identity. Further, f of z, f of z की हमने value अभी find की है, वो आ रहा है, अब</transcript><transcript><audio_21> क्योंकि p terms इधर है, expected value of this. So, each component of z is a standard normal, variate, distributed independently from</transcript><transcript><audio_22> एक्स क्या follow कर रहा था? multivariate normal distribution को तो जो हमने transformation की है which is also follows the multivariate normal distribution को अगर एक्स follow कर रहा है univariate को तो जो हम transformation</transcript><transcript><audio_23> variable भी follow करेगा univariate को, if x follows the multinomial distribution, transformed variable is also follows the multinomial distribution, वो standard normal को follow कर रहा है, तो हमारे पास each of</transcript><transcript><audio_24> multivariate distribution. Each of x follows the standard normal variate distributed independently from each other.</transcript> answer but this is the density function of multivariate normal distribution with mean vector zero and variance covariate.  Matrix identity matrix so Vector Zero End Variance Covariate Matrix Identity Fard f Oz What will be its value becomes 1/2 because p terms here are the expected value of this so each component of z is a standard normal variate distributor independently from each other so what did we do in this x what did we follow the multivariate normal distribution so which  We have done the transformation which is also follows the multivariate normal distribution if x follows the univariate then the variable we are transforming will also follow the univariate if x follows the multinomial distribution transform variable e also follows the  Multinomial distribution is following the standard normal so we have Each of x also follows the standard normal Multivariate distribution Each of x follows the standard normal variate distribution independently from each other
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