1-)The probability intensity function and function are integrated thye random variable with normaldistrubition W. normal distribution probability density. function integral equals 1.wwMWW w Nwwww www w w wm+001| fw (w) dw =e-(w-H)²/20² dw = 1%3D%3D-08- 00a)x = ( w -u)/a the accuracy of the statement below, using the equality show.www1edxV2n-00b) Verify that the following statement is true.I+0012 =-| e-(x*+y°)/2 dxdyc) show that the integral equals 1 by typing the integral in polar coordinates 12MAW MA wwM

Answered: 1-)The probability intensity function…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The joint density function for random variables X and Y is f(x, y). Find the conditional mean and variance of X given Y = 1/2 f(x,y) = 12/7(x^2 + xy) 0<x<1, 0<y<1 0 elsewhere = _mean1/2________________ = _var1/2________________
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A random variable is normally distributed with a mean of μ = 50 and a standard deviation of a = 10. (a) The following figure shows that the normal curve almost touches the horizontal axis at three standard deviations below and at three standard deviations above the mean (in this case at 20 and 80). Areas Under the Curve for any Normal Distribution O O м-30 20 μ-20 30 40 20 40 60 Sketch a normal curve for the probability density function. Label the horizontal axis with values of 20, 30, 40, 50, 60, 70, and 80. 99.7% 95.4% μ-lo н 50 68.3% 60 μ + lo 70 80 A T μ + 20 80 70 50 30 +30 80 X 70 60 50 40 30 20 30 50 70 80 60 40 20 (b) What is the probability the random variable will assume a value between 20 and 80? (Round your answer to three decimal places.) (c) What is the probability the random variable will assume a value between 40 and 60? (Round your answer to three decimal places.)
Continuous random variables 6. A charity group raises funds by collecting waste paper. A skip-full will contain an amount, X of other materials such as plastic bags and rubber bands. X may be regarded as a random varibales with probability density funnction. All nmerical values are in units of 100kg. Find the Expected value and Standard deviation.Express your answer in 3 decimal place value f(x)= - c(x-1)(4-x) 0 for 1
Question * Let X and Y be two continuous random variables with joint probability density (3x function given by: f(x.y)%= 0sysrsl elsewhere 3. E(X')= 3. 3. with E(X) E(Y) = 2, E(Y') = and E(XY)= 10 Then the value of the varianee of X+Y IS. 91/320 3/80 43/320 7/20
Ch: Estimating Random Variables Q: The beta distribution plays an important role in Bayesian statistics. It has two parameters, called shape parameters. Let X and Y be independent uniform random variables on the interval [0,1]. Estimate via simulation the pdf of the maximum of X and Y and compare it to the pdf of a beta distribution with parameters shape1=2 and shape2=1. Use 'dbeta()'. (use R-code)

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