The following code was used to generate the graphs in Figure 9.3.

?Modify the code to illustrate the strong law of large numbers

?for an i.i.d. sequence with the following distributions:?

(i) Pois(? = 5),?

(ii) Norm(?4, 4),?

(iii) Exp(? = 0.01).

Transcribed Image Text:

O 200 400 600 800 1000 O 200 400 600 800 1000 200 400 600 800 1000 O 200 400 600 800 1000 O 200 400 600 800 1000 200 400 600 800 1000 O 200 400 600 800 1000 O 200 400 600 800 1000 O 200 400 600 a00 1000 ebeJony 0.5 0.6 0.7 0.8 0.9 1.0 Average ebeJeny 0.0 0.2 0.4 0.6 0.8 0.3 0.5 0.7 Average Average Average 0.2 0.4 0.6 0.8 1.0 O'L 60 BO 2'0 90 SO SO PO E'o zO L'O 00 abeiany ateiany ebeany O'L 6'0 8'0 L'0 9'0 g'0 9'0 O'L B'0 B0 L'0 9'0 9'O R: STRONG LAW OF LARGE NUMBERS par (mfrow=c (3,3)) > n = 1000 > p = 1/2 > for (i in 1:9) { seg <- rbinom (n, 1,p) # Distribution avgs <- cumsum(seg) / (1:n) plot (avgs, type="1",xlab="n",ylab="Average") abline (h = p) + + +