Binomial distribution. Estimate the number of recursive calls that would be used by the co...

Binomial distribution. Estimate the number of recursive calls that would be used by the code

public static double binomial(int n, int k){   if ((n == 0) && (k == 0)) return 1.0;   if ((n < 0) || (k < 0))   return 0.0;   return (binomial(n-1, k) + binomial(n-1, k−l))/2.0;}

to compute binomial (100, 50). Develop a better implementation that is based on dynamic programming. Hint: See EXERCISE 1.4.41.

EXERCISE 1.4.41.

Binomial coefficients. Write a program that takes an integer command-line argument n and creates a two-dimensional ragged array a[] [] such that a[n] [k] contains the probability that you get exactly k heads when you toss a fair coin n times. These numbers are known as the binomial distribution: if you multiply each element in row i by 2n, you get the binomial coefficients—the coefficients of xk in (x+1)n—arranged in Pascal’s triangle. To compute them, start with a [n] [0] = 0.0 for all n and a[l] [1] = 1.0, then compute values in successive rows, left to right, with a[n][k] = (a[n-l] [k] + a[n-l] [k-1]) / 2.0.