Problem 2.6: A continuous joint probability distribution is expressedthrough the following expression. Find: (a) c, (b) P(X < -0.2, 2 < y < 2.5),(c) P(-4 < X < -0.3), (d) the marginal distributions g(r) and h(y).x+yfor -1

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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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f(x), a continuous probability function, is equal to 1/12, and the function is restricted to 0
3) Find the mean and variance of the random variable X with probability function or density f(x). (a)f(x)={k(1-x), –15xs1 O otherwise (b) ƒ(x) = k/3× , x = 1,2,3,... Note: in this problem, you need to first find the values of k.
suppose x has an exponential distribution with B=1/8 , then P(X>1)
4. The cumulative distribution function of a continuous random variable, X is given as follows: x<0 F(x) = - x(x+4), 32 0Sx<4 1 x24 (a) Calculate P(|X-1|<1). (b) Find the median. (c) Determine the probability density function of X. Hence, evaluate E(3X² -1).
1. Let X be the mean of a random sample of size n = 64 from the exponential distribution e-2/², x>0 otherwise 0, f(x)= = Based on central limit theorem, approximate the probability P (1.8 < X < 2.1). Round your final answer to 4 decimals.
(a) Let X1 ~ x² (n, 8) and X2 ~ x² (m, 1). mX1 and its parameters. nX2 (i) Find the distribution of X = (ii) If 1 = 0, name the distribution of X given in 3(a)(i).
3. A random variable X has a cumulative distribution function if 0 0.5). (e) Find P(X < 1.25). (f) Find P(X = 1.25).
The "kernel trick" is a quick way to integrate when you can recognize a distribution in some equation g(x) which you want to integrate. It takes advantage of the fact that the pdf f(x) of a proper probability distribution must integrate to 1 over the support. Thus if we can manipulate an equation g(x) into the pdf of a known distribution and some multiplying constant c in other words, g(x) = c · f(x) --- then we know that C • --- Saex 9(x)dx = c Smex f(x)dx = c ·1 = c Steps: 1. manipulate equation so that you can recognize the kernel of a distribution (the terms involving x); 2. use the distribution to figure out the normalizing constant; 3. multiply and divide by the distribution's normalizing constant, and rearrange so that inside the integral is the pdf of the new distribution, and outside are the constant terms 4. integrate over the support. The following questions will be much easier if you use the kernel trick, so this question is intended to give you basic practice. QUESTION:…
7. Prove or disprove that the following function is a cumulative distribution function (cdf). If the function is a cdf, is the random variable continuous or discrete? Why? (Note: This is a special case of a logistic distribution.) Fx(x)= 1 1+ e-z -∞<<∞.
6) Probability function of X given as follow; f(x)= 1-(x/2); 0 < x< 2 a. Please draw the graph of the probability function? b. What is the probability of 0 < x < 0,5? c. What is the probability of 0 < x < 2?

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Problem 2.6: A continuous joint probability distribution is expressed through the following expression. Find: (a) c, (b) P(X < -0.2, 2 < y < 2.5), (c) P(-4 < X <-0.3), (d) the marginal distributions g(x) and h(y). r+y for -1