TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Bura)/Übungen 2019W/4.2

Aus VoWi
Zur Navigation springen Zur Suche springen
Coin throws

An unfair coin is thrown 600 times. The probability of geting a tail in each throw is 1/4.

(a) Use a Binomial distribution to compute the probability that the number of heads obtained does not differ more than 10 from 250.
(b) Use a Normal approximation without a continuity correction to calculate the probability in (a). How does the result change if the approimation is provided with a continuity correction?

Lösungsvorschlag von Gittenburg[Bearbeiten | Quelltext bearbeiten]

--Gittenburg 07:17, 4. Nov. 2019 (CET)

(a)

> pbinom(250+10, 600, 3/4) - pbinom(250-10, 600, 3/4)
[1] 5.675012e-61

Eventuell ist das ein Tippfehler in der Angabe und 450 ist gemeint:

> pbinom(450+10, 600, 3/4) - pbinom(450-10, 600, 3/4)
[1] 0.6540917

Lösungsvorschlag von Jeremyer[Bearbeiten | Quelltext bearbeiten]

--Jeremyer 07:17, 9. Nov. 2020(CET)

(b)

> n = 600
> p = 3/4
> q = 1 - p
> a = 450 - 10
> b = 450 + 10

Without continuity correction

> pnorm((b - (n*p))/sqrt(n*p*q)) - pnorm((a - (n*p))/sqrt(n*p*q))
[1] 0.6542214

With continuity correction

> pnorm((b + 0.5 - (n*p))/sqrt(n*p*q)) - pnorm((a - 0.5 - (n*p))/sqrt(n*p*q))
[1] 0.6778012