CQF final - Statistics Project Example

Consider a cantilever beam that has a load that is denoted by F and the load is applied at the end. The beam has a diameter that is denoted by D, this diameter is from the cross-sectional area of the beam and the elastic modulus of the beam is denoted by E. It is a known fact that the elastic modulus of the material changes hence changes from beam to beam. L represents the length and it is a constant for every ten centimeters of the beam. All these will be random inputs of the beam in order to manufacture them.

F is the only random variable, F has, a lognormal distribution, the deflection will have lognormal distribution. But of several variables are random, then the analysis is much more complicated. In order to address this problem we use the sampling approach whereby we assume a distribution function to represent all input variables. Sample variable independently then calculate the deflection from the formula. When this is repeated on many occasions in order to determine and obtain the output distribution.

Assume that we know all the distributions for all input variables. Three input variables will be taken then calculated in order to find out the output distribution. Rand of one gives us one return of random number that is uniformly distributed between zero and one. If you take that and give the force that runs from between 1000 and 1050 newton, you take the minimum value that is 1000 newton and add fifty times that random number that is between zero and one which will give us a number between zero and fifty with equal probability line between them.

For all the other variables, this will take place for all values that include the diameter and inertia. This involves making a decision as to how many samples are required which gives the random n samples which in return are a vector of uniformly distributed numbers between zero and one which give uniformly distributed forces which are 100000 forces all in one command. Now that the