import torch


def lincomb_norm_mean(mean: torch.Tensor, coeff: torch.Tensor) -> torch.Tensor:
    """Returns the means for w linear combinations of n normal distributions

    Args:
        mean (torch.Tensor): n-vector where the i-th entry corresponds to the
          i-th distribution mean
        coeff (torch.Tensor): w-by-n matrix where the (i, j) entry corresponds
          to the i-th set and j-th coefficient for the j-th distribution

    Returns:
        torch.Tensor: w-vector where the i-th entry corresponds to the i-th
        distribution mean
    """
    return (mean[None, :] @ coeff.T)[0, :]