# Section 4; Question 1: # p = 0.3 print( 1 - ( p + p*(1-p) + p*(1-p)^2 ) ) # Section 4; Question 3: # source('chap_4_sect_4_question_3_data.R') T = table(data) empirical = T/length(data) ks = 1:max(data) model = 0.25 * 0.75^(ks-1) print( data.frame( k=ks, empirical=as.double( empirical ), model=as.double( round( model, 2 ) ) ) ) # Section 4; Question 6: # n_mc = 100000 die_1 = sample( 1:6, n_mc, replace=TRUE ) die_2 = sample( 1:6, n_mc, replace=TRUE ) die_3 = sample( 1:6, n_mc, replace=TRUE ) sum_is_four = sum( (die_1 + die_2 + die_3) == 4 ) p_exact = 1/72 print( sprintf("MC= %f; exact= %f", sum_is_four / n_mc, p_exact ) ) F_X = function(x){ 1 - (1-p_exact)^x } print( sprintf("Prob= %f", F_X(75) - F_X(64)) )