Question

El número de supervivientes según tablas de las generaciones 2002, 1997,1992 son para un grupo de tres personas X,Y Z de 35, 40 y 45 años serán en el año 2037

	Generación 2002	Generación 1997	Generación 1992
	\(l_{35}\)=3000	\(l_{40}\)=2000	\(l_{45}\)=4000
	\(l_{65}\)=2979	\(l_{70}\)=1950	\(l_{75}\)=3780

Hallar las siguientes probabilidades en los siguientes 30 años

Answerlist

• probabilidad de No extinción?
• probabilidad disolución y no extinción?
• probabilidad de disolución ?
• probabilidad de sobreviva como máximo dos?
• probabilidad sobrevivan al menos dos?

Solution

\[ p_{x}=\frac{l_{65}}{l_{35}}=\frac{2979}{3000}={0.993}\hspace{1cm} p_{y}=\frac{l_{70}}{l_{40}}=\frac{1950}{2000}={0.975}\hspace{1cm} p_{z}=\frac{l_{75}}{l_{45}}=\frac{3780}{4000}={0.945} \\ q_{x}={0.007}\hspace{1cm} q_{y}={0.025}\hspace{1cm} q_{z}={0.055}\\ \text{Extinción} =q_{x}·q_{y}·q_{z}={0.007}·{0.025}·{0.055}={10^{-5}}\\ \text{No extinción}= 1- extinción=1-(q_{x}·q_{y}·q_{z})=1-({0.007}·{0.025}·{0.055})=1-{10^{-5}}={0.99999}\\ \text{Disolución y No extinción}=\text{Disolución - Extinción}= (((1-(p_{x}·p_{y}·p_{z}))-(q_{x}·q_{y}·q_{z}))\\ ={0.085075}-{10^{-5}}={0.085065}\\ \text{Disolución}= _{n}q_{xyz}=1-_{n}p_{xyz}=(1-(p_{x}·p_{y}·p_{z}))=1-(super conjunta)=1-({0.993}·{0.975}·{0.945})=\\=1-{0.914925}={0.085075}\\ \text{sobrevivan max 2, tambien disolucion alguno muere incluso los 3}= _{n}p_{\bar{xyz}2}=1- super conjunta= 1-({0.993}·{0.975}·{0.945})={0.085075}\\ \text{sobrevivan al menos 2}= _{n}p_{\bar{2xyz}}=(p_{x}·p_{y}·q_{z})+(p_{y}·p_{z}·q_{x})+(p_{z}·p_{x}·q_{y})+(p_{x}·p_{y}·p_{z})=\\ (({0.993}·{0.975}·{0.055})+({0.975}·{0.945}·{0.007})+({0.945}·{0.993}·{0.025})+({0.993}·{0.975}·{0.945}))={0.9980839} \]

Answerlist

• probabilidad de NO extinción \(0.99999\).
• disolución y No extinción \(0.085065\).
• disolución \(0.085075\).
• sobreviva máximo dos \(0.085075\)
• sobrevivan al menos dos \(0.998084\)

Meta-information

extype: cloze exclozetype: verbatim|verbatim exsolution: :NUMERICAL:=0.99999:0.1~%50%0.99999:0.1#Normal-based instead of t-based interval; for small samples, intervals based on the normal approximation are too narrow.|:NUMERICAL:=0.085065:0.1~%50%0.085065:0.1#Normal-based instead of t-based interval; for small samples, intervals based on the normal approximation are too narrow.|:NUMERICAL:=0.085075:0.1~%50%0.085075:0.1#Normal-based instead of t-based interval; for small samples, intervals based on the normal approximation are too narrow.|:NUMERICAL:=0.085075:0.1~%50%0.085075:0.1#Normal-based instead of t-based interval; for small samples, intervals based on the normal approximation are too narrow.|:NUMERICAL:=0.998084:0.1~%50%0.998084:0.1#Normal-based instead of t-based interval; for small samples, intervals based on the normal approximation are too narrow. exname: Confidence interval extol: 0.01