# Simulation of a function of normal, uniform, and exponential random variables [closed]

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, ShaileshDec 28 '17 at 1:49

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, Namaste, BruceET, Jean Marie, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.

• 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. – Jean Marie Dec 27 '17 at 23:20
• 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. – Jean Marie Dec 27 '17 at 23:25
• No answer. I vote to close this question. – Jean Marie Dec 28 '17 at 1:20
• this is an assignment, with any simulator based on Monti Carlo methods – Ayman Dec 28 '17 at 22:35
• You come back a day after you have asked your question : it's not serious... – Jean Marie Dec 28 '17 at 23:09

## 1 Answer

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
mean(t)
## 13434.11


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

• this is an assignment, with any simulator based on Monti Carlo methods – Ayman Dec 28 '17 at 22:35
• 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. – BruceET Dec 28 '17 at 23:36