Shree GaneshA Statistics

Probability Distribution.   Normal Distribution: Normal distribution is the maximally used Probability distribution in the theory of statistics.    Definition : A Random variable X is used said to be follow a normal distribution with mean m and variance   σ 2   then its probability density function is  f(x) =  the variable x is said to be normally distributed with mean m and  variance   σ 2    then it is denoted as  X  ~ N(m , σ 2  ). and if in normal distribution the values of parameter changes as m= 0 and  σ 2  = 1 then distribution of x is said to be standard normal distribution and it is denoted as  X  ~ N(0 ,1  ).   if  X  ~ N(m , σ 2  ). and we take transformation as z = (x-m)/ σ then the distribution of z is standard normal distribution. and it is denoted as Z   ~ N(0 ,1  ).  the pdf of f(z) is called standard normal distribution  a...

 Probability:  Basic concepts of Probability:  Probability is a way to measure hoe likely something is to happen. Probability is number between 0 and 1, where probability is 0 means is not happen at all and probability is 1 means it will be definitely happen, e.g. if we tossed coin there is a 50% chance to get head and 50% chance to get tail, it can be represented in probability as 0.5 for each outcome to get head and tail. Probability is used to help us taking decision and predicting the likelihood of the event in many areas, that are science, finance and Statistics.  Now we learn the some basic concepts that used in Probability:  i) Random Experiment OR Trail: A Random Experiment is an process that get one or more possible outcomes. examples of random experiment include tossing a coin, rolling a die, drawing  a card from pack of card etc. using this we specify the possible outcomes known as sample pace.  ii)Outcome: An outcome is a result of experi...

 Statistical quality control.: Control  chart for Number of Defects (C-chart) A C chart is a one type of chart in Statistical quality control (SQC)  to monitor the count or frequency of nonconforming items. it is particularly  used when dealing with discrete data or attribute data, where the outcomes are classified in to defective or non defectives or (conforming or nonconforming). The Primary use of c chart is to monitor the number of defects or nonconforming items in a production or manufacturing process. it helps to identify the the trend of defectives in a process to take decision and action regarding the production process. this allows the continuous improvement in the production process.  A C chart is also useful   for tracking and monitoring the occurrence of  defects over  a time. it allows to identify periods or specific factors that contributes to increasing number of  defects. The C chart helps to evaluate the effectiveness of...