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  and defined as  note :  1 mean of the distribution is m. 2. the variance of the distribution is  σ 2   3. the shape of normal distribution is bell-sha

 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 experiment. an outcome is one of the pos

 Non- Parametric test Median test Median test is also a Non-Parametric test and it is alternative to Parametric T test. The median test is used when we are interested to check the two independent sample have same median or not. It is useful when data is discrete or continuous and if data is in small size.  Assumptions:  I) the variable under study is ordinal scale II) the variable is random and Independent. The stepwise procedure for computation of median test for two independent sample : Step I :- firstly we define the hypothesis Null Hypothesis is the two independent sample have same median.  Against Alternative Hypothesis is the two independent sample have different median.  Step II :- In this step we combine two sample data. And calculating the median of combined data. Step III :- after that for testing hypothesis we constructing the (2x2) contingency table. For that table we divide the sample into two parts as number of observation above and below to the median for both sample t