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Answer: Hi Pradeep, Yes both are the measure of spread around the mean. However, their units are different. Unit of variance is the square of the unit of the data whereas the unit of standard deviation is same as that of data. The mean is also having the same unit that of data. This is sometime helpful when you are looking for the deviation from the mean. We also calculate coefficient of variation (CV), which is the ratio of standard deviation and mean. This is dimensionless as standard deviation and mean are having the same unit. Being dimensionless, we can easily compare CVs for two different datasets. Hope this helps your query.

Answer: There is an analogy between moment in physics and moment in probability theory. Moment in physics is a representation of the distribution of any physical quantity with respect to an axis. Similarly, moment in probability theory is the distribution of the data points or ‘probability mass’ with respect to some point (location). As we know that mean is located at the centroid (‘centre of gravity’ while making an analogy with physics) of the probability distribution, the first moment with respect to the mean is zero. First moment with respect to the origin expresses the location of the mean, i.e. distance of the centroid from the origin. Higher order moments are generally expressed with respect to the mean as they have some meaningful representation of the nature of the distribution. For instance, second moment with respect to the mean expresses the spread of the distribution function about the mean. This is used as variance. Similarly third and fourth moment with respect to the me

Answer: Did you mean 'Mean Square Error (MSE)' or 'Root Mean Square Error (RMSE)'? These are the measures of difference between estimated values and its true values. Lower the values of MSE or RMSE better the estimated values.

Answer: Yes there are many books. Some of them are listed in the reference list of the course. However, all of them may not have the corresponding MATLAB demonstration. You may send your queries to me. If I know the MATLAB command, I will help you.

Answer: Concept of reliability is based on the probability theory. Reliability based design aims to minimize the probability of failure. Thus, reliability based design methods are more specific compare to general probability methods; however, based on the theory of probability.

Answer: Please contact through email sushanta_cet@yahoo.co.in He may guide you or tell whom to contact

Answer: Examples on general probability methods are included in the course material. Please refer to the solved problems.

Answer: Dear Elangovan, I doubt whether I understood the context of your query. In the lecture, it was discussed in a general context. The problem of uncertainty in estimating the loads and other factors needs a probabilistic representation. This is generally represented separately for different attributes, i.e., applied load, material properties, uncertainties in construction etc.

Answer: Hi Pradeep, Yes both are the measure of spread around the mean. However, their units are different. Unit of variance is the square of the unit of the data whereas the unit of standard deviation is same as that of data. The mean is also having the same unit that of data. This is sometime helpful when you are looking for the deviation from the mean. We also calculate coefficient of variation (CV), which is the ratio of standard deviation and mean. This is dimensionless as standard deviation and mean are having the same unit. Being dimensionless, we can easily compare CVs for two different datasets. Hope this helps your query.

Answer: There is an analogy between moment in physics and moment in probability theory. Moment in physics is a representation of the distribution of any physical quantity with respect to an axis. Similarly, moment in probability theory is the distribution of the data points or ‘probability mass’ with respect to some point (location). As we know that mean is located at the centroid (‘centre of gravity’ while making an analogy with physics) of the probability distribution, the first moment with respect to the mean is zero. First moment with respect to the origin expresses the location of the mean, i.e. distance of the centroid from the origin. Higher order moments are generally expressed with respect to the mean as they have some meaningful representation of the nature of the distribution. For instance, second moment with respect to the mean expresses the spread of the distribution function about the mean. This is used as variance. Similarly third and fourth moment with respect to the me

Answer: Did you mean 'Mean Square Error (MSE)' or 'Root Mean Square Error (RMSE)'? These are the measures of difference between estimated values and its true values. Lower the values of MSE or RMSE better the estimated values.

Answer: Yes there are many books. Some of them are listed in the reference list of the course. However, all of them may not have the corresponding MATLAB demonstration. You may send your queries to me. If I know the MATLAB command, I will help you.

Answer: Concept of reliability is based on the probability theory. Reliability based design aims to minimize the probability of failure. Thus, reliability based design methods are more specific compare to general probability methods; however, based on the theory of probability.

Answer: Please contact through email sushanta_cet@yahoo.co.in He may guide you or tell whom to contact

Answer: Examples on general probability methods are included in the course material. Please refer to the solved problems.

Answer: Dear Elangovan, I doubt whether I understood the context of your query. In the lecture, it was discussed in a general context. The problem of uncertainty in estimating the loads and other factors needs a probabilistic representation. This is generally represented separately for different attributes, i.e., applied load, material properties, uncertainties in construction etc.