Question

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 1^st and 99^th percentile of the taller of the man and woman, that is, estimateassociated with Y = max {X1, X2}. Use 1000 simulated pairs.

Answer 1

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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