KADD 2022 Laboratorium 3 EN

From Łukasz Graczykowski

Contents 1 Task 2 Attention 3 Results

Task

We have a probability distribution function given with the following formula:

For parameters m=1 and n=2 please:

• calculate c so that the distribution is normalized (1pkt)
• draw probability distribution function f(x,y) (1pkt)
• draw cumulative distribution F(x,y) (1pkt)
• draw marginal distribution g(x) (1pkt)
• draw marginal distribution h(y) (1pkt)

Attention

• All quantities (constant c, cumulative distribution, marginal distributions) we calculate numerically, i.e. by using Integral method.
• The script has to be written in a way Skrypt powienien być napisany w taki sposób aby wykonywał obliczenia dla dowolnego m i n.
• Please name correctly all axes.
• The probability function (TF2 object) we create by using a proper constructor which includes a pointer to the function (appropriately defined for all values x and y):

double fcn(double *x, double *params)

TF2(const char* name, void* fcn, Double_t xmin = 0, Double_t xmax = 1, Double_t ymin = 0, Double_t ymax = 1, Int_t npar = 0)

Example:

double function(double *x, double *params)
{
   if(x[0]>=0 && x[1]>=0)
     return params[0]*x[0]*x[1];
   return 0;
}
...
double xmin = 0;
double xmax = 10;
double ymin = 0;
double xmax = 10;
int nparams = 1;
TF2 * fun1 = new TF2("fun1",function,xmin,xmax,ymin,ymax,nparams);

Results

Plots:

Output:

Normalization factor c=6