In this video, the concepts in estimation theory introduced so far for scalar random variables are extended to deal with estimating multiple parameters, for example the mean and variance of a distribution simultaneously. The definition of a vector parameter estimator is introduced, and the example of extending the definition of bias. The principal focus of the video is on extending the Cramer-Rao Lower Bound (CRLB) to real parameter vectors, by placing a bound on the covariance matrix of the estimator. Parallels with the scalar CRLB are made throughout, but the emphasis is on the key calculation of the Fisher Information matrix (FIM). This is the expectation of functions of the derivatives of the log-likelihood function, but considering the derivatives with respect to all the elements of the parameter vector. Finally, the line-fitting example of estimating the parameters of a straight line to fit a set of data that is assumed to follow a linear model. The FIM and CRLB are calculated, and it is shown that in this case the minimum variance unbiased estimator (MVUE) can be found as before. Numerical simulations are also provided to demonstrate the correctness of the calculations.