Advanced High-School Mathematics

354 CHAPTER 6 Inferential Statistics

(b) EstimateP(. 5 ≤Z ≤ 1 .65) through a simulation, using the

TI code as follows. (I would suggest takingN ≥100 trials in

this simulation.)

PROGRAM: SIMUL1

:0→C

:INPUT “N: ”, N

:For(I,1,N)

:rand + rand→Z

:C+ (. 5 ≤Z)(Z≤ 1 .65)→C

:END

:DISP “PROB: ”, C/N

:STOP

The quantityC/N is the estimated probability!

(c) Construct a histogram for 100 observations of the random

variableZ. Try the following code (using, say,N = 100):

PROGRAM: SIMUL2

:INPUT “N: ”, N

:{ 0 }→L 1

:For(I,1,N)

:rand + rand→L 1 (I)

:END

Once you’ve done the above, you then use your graphing cal-

culator to graph the histogram of the list variableL 1. (You’ll

need to decide on sensible window settings.)

3. LetBandC be uniform random variables on the interval [− 1 ,1].
   (Therefore B andC are independent occurrences of 2rand−1.)
   Compute
   (a) the probability that the quadraticx^2 +Bx+C = 0 has two
   distinct real roots;
   (b) the probability that the quadraticx^2 +Bx+C= 0 has a single
   multiple root;