TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Bura)/Übungen 2019W/2.1

Based on its analysis of the future demand for its products, the financial department at a certain corporation has determined that there is a 0.17 probability that the company will lose 1.2 million dollars during the next year, a 0.21 probability that it will lose 0.7 million dollars, a 0.37 probability that it will make a profit of 0.9 million dollars, and a 0.25 probability that it will make a profit of 2.3 million dollars.

(a) Let X be a random variable that denotes the profit (in million dollars) earned by this corporation during the next year. Write the probability distribution of X.

(b) Find the mean and standard deviation of the probability distribution of part (a).

(c) Give a brief interpretation of the value of the mean.

(d) Compute P (|X| ≤ 1) and Fx (1.5), where Fx (x) is the cumulative distribution function (cdf) of X.

Lösungsvorschlag von Gittenburg

--Gittenburg 18:06, 21. Okt. 2019 (CEST)

(a)

x = c(-1.2, -0.7, 0.9, 2.3)
px = c(0.17, 0.21, 0.37, 0.25)

(b)

> e = sum(x * px)
> e
[1] 0.557
> var = sum((x - e)^2 * px)
> var
[1] 1.659651
> sd = sqrt(var)
> sd
[1] 1.288274

(c) Wenn die Firme dieselben Gewinnwahrscheinlichkeiten für einige Jahre beibehält, kann sie im Durchschnitt mit 557,000$ Profit rechnen.

(d) $P(|X|\leq 1)=0.21+0.37$

$F_{X}(1.5)=0.17+0.21+0.37$