Show that two random variables X, and X, with joint pdf,16.1|x, |< 4, 2

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Answered: Show that two random variables X, and…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let X1, X2, X3 be independent normal random variables which all have mean 9 and standard deviation 1.2. 1) a) Calculate the mean of X1 + 5X2 – 3X3 . Number (exact value) b) State the standard deviation of X1 + 5X2 – 3X3. Number (enter your answer correct to at least 3 decimal places) c) State P(X1 + 5X2 - 3X3 9.72) AA (enter your answer correct to at least 3 significant figures) b) Find P(X1 > 9.72 | X1 > 8.4) AE (enter your answer correct to at least 3 significant figures) c) State P(X1 > 9.72|X2 > 8.4) AE (enter your answer correct to at least 3 significant figures)
A random variable X~Binomial (2, 1/3) is chosen, but the result is badly recorded; the record Y has an equal chance of being X, X+1, or X+2. a) Find the joint PMF of X and Y. Y=0 Y=1 Y=2 Y=3 Y=4 X=0 X=1 X=2 b) Find the conditional PMF of X given Y. Y=0 Y=1 Y=2 Y=3 Y=4 X=0 X=1 X=2 c) The Y=2 column of your second table should match the marginal distribution of X. What does this say about how useful a record of "Y=2" in telling you the actual value of X?
4. In professor Shankar's quiz, the time taken to complete the quiz is a random variable with a pdf £x (x) = 20 = exp(-26 ) ₁ x 20² 20 1₂x ≥0 What is the average time for completion? If there are 50 students in the class, what is the probability that at least 20 of them will complete the quiz in less than the average? What is the probability that exactly 35 students complete within the average time.
If X is a random variable in the range 1≥x≥0, and f(x) = k(x^4-2), then the value of k is 1- 3/5 2-5/3 3-15 4-5 Select one option
Suppose that W is a (a = 3, 3 = })-gamma random variable and N is a µ = -Poisson random variable independent of W. What is E (w*]? un for u-Poisson random variable N. n! Note: PN (n) = P (N = n) = e Hint: pmf for a (r, p)-negative binomial random variable is given by n - n = r,r + 1,... r - 1
12. Suppose (1, 2, ..., n) is a random sample from ...,n) is a random sample from a normal distribution, find the absolute efficiency of the maximum likelihood estimator of 0 if, x; ~ ~ N(0, 1).
6
assume X~ Binomial witth P =ų and Find the max Likle hood estimator.
Suppose that discrete random variable X~uni[1,2,3] A random sample of n=36 is selected from this population. Find the probability that the sample mean is greater than 2.1 but less than 2.5, assuming that the sample mean would be measured to the nearest tenth.
Exercise 3: Find MVUE for 0, in each of the following cases: 1. (X1, X2, ... ,Xx,} is a random sample from Gamma(4,0). 2. (X1, X2, ... ,X,} is a random sample from Binomial (10, 0). 3. (X1, X2, ...,Xx,} is a random sample from Poisson(0).
An insurance company has an initial surplus of 100 and premium loading factor of 20%. Assume that claims arrive according to a Poisson process with parameter \ 5 and the size of claims Xį are iid random variables with Xi exp(). The time unit is 1 week. Assume that 1 month = is 4 weeks. (a) Calculate the average number of claims on any given day, week and month. Let t'> 0 be an instance of time. Calculate the probability that at least one claim occurs within 5 days after t'. Calculate also the probability that at least 2 claims occur within 5 days after t'. (b) Let t = 2 months. Calculate the mean and variance of S(t) and of U(t), where (S(r))ro and (U(r))rzo are the aggregate claim process and the surplus process of the described model.
You have two random variables M and N where the joint pdf is given by f_M,N(m,n) = 1/2 if m + n >=2, m <=2 and n <=2 and 0 o/w. What is the cdf?

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Show that two random variables X, and X, with joint pdf, 1 |x, < 4, 2