A Pen for Liberation

  Normal distribution is one of the most important continuous probability distributions occuring in many aspects. We explore its properties and applications in this thread. Normal distributions are symmetric, unimodal, and asymptotic, and the mean, median, and mode are all equal. A normal distribution is perfectly symmetrical around its center. That is, the right side of the center is a mirror image of the left side. The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1. The standard normal distribution is centered at zero and the degree to which a given measurement deviates from the mean is given by the standard deviation. Importance of Normal Distribution 1. Many classical statistical tests are based on the assumption that the data follow a normal distribution. This assumption should be tested before applying these tests. 2. In modeling applications, such as linear and non-linear regression, the error term is often assumed to foll

  A sequence is called an arithmetic progression of the first order if the differences of the successive terms are constant. It is called an arithmetic progression of the second order if the differences of the successive terms form an arithmetic progression of the first order. In general, for k ≥ 2, a sequence is called an arithmetic progression of the k-th order if the differences of the successive terms form an arithmetic progression of the (k-1)-th order.