5.44 Assume that men’s heights, in inches, are N(70, 16) random variables, and women’s heights, in inches, are N(67, 9) random variables. Let X1be the height of a man and X2 be the height of a woman selected at random. Conduct a Monte Carlo simulation experiment in R to estimate the 1st and 99th percentile of the taller of the man and woman, that is, estimateassociated with Y = max {X1, X2}. Use 1000 simulated pairs.
ANSWER::
Solution :-
A random variable for height of men from normal distribution with
mean 70 and standard-deviation 16.
A random variable for height of women from normal distribution with
mean 67 and standard-deviation 9.
Lets generate
through Mounte Carlo process in R-
R -code-
x_1=rnorm(1000,70,16)
Lets generate
through Mounte Carlo process in R-
R -code-
x_2=rnorm(1000,67,9)
Now lets find out pair wise maximam value for these thousand x_1 ans x_2 random-variables and lets name it x_3.
R-code-
x_3=pmax(x_1,x_2)
Now finding the 1 and 99 percentile for x_3-
R-code-
quantile(x_3, c(.01, .99))
Result-
quantile(x_3, c(.01, .99))
1% 99%
55.28309 108.15056
(OR) TRY THIS ANSWER
R code-
Y=0
for(i in 1:1000)
{
X1=rnorm(1,70,4)
X2=rnorm(1,67,3)
Y[i]=max(X1,X2)
}
quantile(Y,c(0.01,0.99))
Output-
1% 99% 63.78987 78.55482
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5.44 Assume that men’s heights, in inches, are N(70, 16) random variables, and women’s heights, in...
Assume thats men's heights, in inches, are N(70, 16) random variables, and women's heights, in inches, are N(67,9) random variables. Let X1 be the height of a man and X2 be the height of a women selected at random. Conduct a Monte Carlo simulation experiment in R to estimate the 1st and 99th percentile of the taller of the man and woman, that is, estimate y0.01 and 7.99 associated with Y = max(X1, X2). Use 1000 simulated pairs.
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