I need to solve this please Let $A$ be a normal random variable with $\mu = 70$ and $\sigma= 15$, $B$ a normal random variable with $\mu = 20$ and $\sigma= 3$, $C$ an exponential random variable with $\lambda= 4$, and $D$ a uniform random variable on the interval $[0,1]$. Consider the model $T = 4A^2 - (B/C) + 10D$

Use Monte Carlo simulation method with number of trials (or iteration) equals 1000 to estimate 1. $P(-22.325 < T < 256.458).$ 2. the mean of $T$.


closed as off-topic by Did, Namaste, BruceET, Jean Marie, Shailesh Dec 28 '17 at 1:49

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    $\begingroup$ Welcome to Math Stack Exchange. Can you tell what you have attempted to solve your problem, where you are blocked, etc.? We don't want to serve a solution on a tray without some effort from the asker. $\endgroup$ – Jean Marie Dec 27 '17 at 23:20
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    $\begingroup$ To your question, I reply by questions: what simulation language do you use ? How do you simulate an exponential variable with $\lambda = 4$ (do you know that is done using the logarithm of a certain uniform random variable ?) etc. $\endgroup$ – Jean Marie Dec 27 '17 at 23:25
  • $\begingroup$ No answer. I vote to close this question. $\endgroup$ – Jean Marie Dec 28 '17 at 1:20
  • $\begingroup$ this is an assignment, with any simulator based on Monti Carlo methods $\endgroup$ – Ayman Dec 28 '17 at 22:35
  • $\begingroup$ You come back a day after you have asked your question : it's not serious... $\endgroup$ – Jean Marie Dec 28 '17 at 23:09

I will try to get you started on this by showing a simulation in R statistical software. I used a million trials rather than the requested 1000. I am assuming $\lambda = 4$ is the exponential rate, not the exponential mean.

Because you have shown noting to reveal the level, methods, or computer language of your course, I have no way of knowing whether this is helpful.

 set.seed(1227);  m = 10^6
 a = rnorm(m, 70, 15);  b = rnorm(m, 20, 3)
 c = rexp(m, rate=4);   d = runif(m, 0, 1)
 t = 4*a^2 - b/c + 10*d
 mean((t > -22.325) & (t < 256.485))
 ## 0.000154
 ## 13434.11

An exponential distribution puts much of its probability near 0. What difficulties do you suppose that might present?

  • $\begingroup$ this is an assignment, with any simulator based on Monti Carlo methods $\endgroup$ – Ayman Dec 28 '17 at 22:35
  • $\begingroup$ So is my Answer helpful? // @JeanMarie asked about metnods: For example, are you supposed to simulate exponential RVs vis uniform, or is it OK to use a function such as R's rexp for that? Similarly for rnorm? Unless you show some attempt to solve the problem, it is difficult for us to give useful answers. $\endgroup$ – BruceET Dec 28 '17 at 23:36

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