newrek2

ZADANIE 1////
#include <stdio.h>

unsigned int newton(unsigned int, unsigned int);

int main(){
    unsigned int n, k;
    printf("Podaj n: ");
    scanf("%d", &n);
    for(k = 0; k <= n; k++) printf("%d ", newton(n,k));
    return 0;
}

unsigned int newton(unsigned int n, unsigned int k){
    if(k == 0 || k == n) return 1;
    else return newton(n-1,k) + newton(n-1,k-1);

}

ZAD 2////

#include <stdio.h>

unsigned int newton(unsigned int, unsigned int);
double Ksukcesow(unsigned int, unsigned int, double, double);

int main(){
    unsigned int n, k;
    double p, q;
    printf("Podaj liczbe prob: ");
    scanf("%d", &n);
    printf("Podaj liczbe sukcesow: ");
    scanf("%d", &k);
    do{
    printf("Podaj prawdopodobienstwo: (p nalezy do <0,1>) ");
    scanf("%lf", &p);
    }while(p < 0 || p > 1);
    q = 1-p;

    printf("Prawdopodobienstwo %d sukcesow w %d probach wynosi: %lf", k, n, Ksukcesow(n, k, p, q));
    return 0;
}

unsigned int newton(unsigned int n, unsigned int k){
    if(k == 0 || k == n) return 1;
    else return newton(n-1,k) + newton(n-1,k-1);

}
double Ksukcesow(unsigned int n, unsigned int k, double p, double q){
    //potegowanie p
    int i;
    double pot = 1;
    double pot2 = 1;
    for(i = 0; i < k; i++) pot*=p;
    for(i = 0; i < n-k; i++) pot2*=q;

    return newton(n,k) * pot * pot2;

}

ZAD3 ////
#include <stdio.h>

unsigned int newton(unsigned int, unsigned int);
double Cumulative(unsigned int, unsigned int, double, double);

int main(){
    unsigned int n, k;
    double p, q;
    printf("Podaj liczbe prob: ");
    scanf("%d", &n);
    printf("Podaj liczbe sukcesow: ");
    scanf("%d", &k);
    do{
    printf("Podaj prawdopodobienstwo: (p nalezy do <0,1>) ");
    scanf("%lf", &p);
    }while(p < 0 || p > 1);
    q = 1-p;

    printf("Prawdopodobienstwo %d lub mniej sukcesow w %d probach wynosi: %lf", k, n, Cumulative(n, k, p, q));
    return 0;
}

unsigned int newton(unsigned int n, unsigned int k){
    if(k == 0 || k == n) return 1;
    else return newton(n-1,k) + newton(n-1,k-1);

}
double Cumulative(unsigned int n, unsigned int k, double p, double q){
    //potegowanie p
    int i;
    double wynik = 0;
    double pot = 1;
    double pot2 = 1;
    for(i = 0; i < k; i++) pot*=p;
    for(i = 0; i < n-k; i++) pot2*=q;

    for(i = 0; i <= k; i++)    wynik+=newton(n,i) * pot * pot2;

    return wynik;

}

/////ZAD 4

#include <stdio.h>
#include <math.h>
double Hoeffding(unsigned int, unsigned int, double);

int main(void){
unsigned int n, k;
double p;
printf("Podaj n,k p: ");
scanf("%d", &n);
scanf("%d", &k);
scanf("%lf", &p);
printf("%lf", Hoeffding(k,n,p));
}

double Hoeffding(unsigned int k, unsigned int n, double p){

return exp((-2/n) * pow(n*p-k, 2));
}

//ZADANIE 5

#include <stdio.h>
#define MAX 100
int tab[MAX][MAX];

int newton(int n, int k){

int i, j;

for(i = 1; i < MAX; i++){

    for(j = 0; j < MAX; j++){

        tab[i][j] = 0;
    }
}

for(i = 0; i < MAX; i++) tab[i][0] = 1; //zerowa kolumna
for(i = 0; i < MAX; i++) tab[i][i] = 1; //diagonala

for(i = 1; i < MAX; i++){

    for(j = 1; j < MAX; j++){

        tab[i][j] = tab[i-1][j-1] + tab[i-1][j];
    }
}

return tab[n][k];

}

int main(void){
    int n, k;
    printf("Podaj n i k: ");
    scanf("%d%d", &n, &k);
    printf("%d", newton(n, k));

    return 0;
}