Consider that a ball is thrown with a random angle ? ∈[0,360) (in degrees) and a random radius ?∈[0,1] (in meters) both independent and uniform. Calculate the density of the variables ? and ? (the cartesian coordinates of the point at angle ? and radius ?) as well as their

Consider that a ball is thrown with a random angle ? ∈[0,360) (in degrees) and a random radius ?∈[0,1] (in meters) both independent and uniform. Calculate the density of the variables ? and ? (the cartesian coordinates of the point at angle ? and radius ?) as well as their

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: 1) Evaluate whether y, and y, are uncorrelated 2) Evaluate whether y, and y, are independent

A: Given, y1y2 = 111-1x1x2 So, y1 = x1+x2y2 = x1-x2 And, Mean is 0 and Variance is 1 So, E(xi) =0…

Q: d) Calculate the sample variance of x. e) Calculate the interquartile range of x, using R. f)…

Q: (b) Define the normal space.

Q: I. R^2 is the square of correlation coefficient I. The type II error of a test is the probability of…

Q: Assume that ? is a random variable has a gamma distribution with (alpha) = 3 and (beta) = 10. A)…

A: Here alpha = 3 , beta = 10 Mean = 3×10 = 30 Standard deviation = 10 √3 = 17.32

Q: Mx Sb sa e -e (5)- s16-a) X~U(a,b) , Calculate the variance of the random variable X.

A: Given mgf of Uniform distribution function, we need to find Variance

Q: Normal distribution. The moment generating function of a random variable U is M(t) = (1 -…

Q: Define rayleigh density and distribution function and explain them with thei plots.

Q: (X, Y)~ Beta(01, 02, 03). Find the expected value and the variance of Y.

A: The joint probability density function of (X, Y) under the Beta distribution is given by: f(x,y) =…

Q: In order to perform the Ansari-Bradley test what must one do first to the data? Rank the data…

A: The AB test is an alternative to the 2 sample F test of equal variances.

Q: Assume that females have pulse rates that are normally distributed with a mean of μ = 76.0 beats per…

A: The question is about normal distribution Given : Popl. mean pulse rate of females ( μ ) = 76 beats…

Q: (Sample Mean and Sample Standard Deviation) Suppose we are given sample data x of size N drawn from…

Q: Prove that the standard deviation of a normal distribution that has parameters (µ , σ) is σ

A: µ (mu): This represents the mean of the normal distribution.σ (sigma): This represents the standard…

Q: d help with part and b and c. I added the data and

A: a) mean = ∑xn = 328.120=16.405 b) variance = ∑(x-xi)2 = 1863.4495 X (mean-x)^2 0 298.1983657…

Q: Suppose X ~ a) Find the expected value of the cost per loss, E [Y,]. b) Find the Variance of the…

A: Given X~Parα=4, θ=300 with d=20

Q: 6. . Suppose that Y,,Y,..Y, form a random sample from a distribution for which the p.d.f. is as…

A: Given that, if Y1, Y2, ...Yn form a random sample from a distribution for which the pdf is given as…

Q: The built-in data set mtcars compares 11 aspects of automobile design 32 different 1974 model…

A: We have to use the mtcars data of R. Since you have posted a question with multiple subparts, we…

Q: Time (minutes) 30-32 33-37 38-44 45-47 Frequency 9. 14 3 a Frequency Density 3 4 1

Q: b) A procurement specialist purchased 28 resistors at random from Supplier 1 and 32 resistors from…

A: It is given that: For Supplier-1:μ1population mean=105σ1population standard deviation=1.58n1 sample…

Q: The random variable Y has normal distribution with a mean of 30 and a variance of 16, i.e. Y~ N(30,…

A: Given,

Q: Suppose the force acting on a column that helps to support a building is normally distributed with…

A: The objective of this question is to find the probability of certain events occurring given a normal…

Q: Residuals are the O a) O horizontal deviations from the line of best fit to each data point b)…

A: Residuals in statistics are the vertical distance, which is measured from the data point to the…

Q: Find (by inspection) the expected values and variances of the exponential random variables with the…

A: it is given that x is a exponential random variables with pdf, a) fx = 3e-3x b) fx = 14e-x4

Q: Assume that females have pulse rates that are normally distributed with a mean of μ=72.0 beats per…

A: Given datanormal distributionμ=72σ=12.5

Q: The built-in data set, rock, is a data frame recording the measurements of rock sample from a…

A: In this case, the built-in data set, rock. Also assume that the n area measurements x=x1,x2,...,xn…

Q: In the thuesen data set from the ISWR package, use R. to perform the following analyses. (a) Subset…

A: R is a programming language and it is used for statistical analysis.

Q: a) Using integrals, directly calculate the variance of the Weibull distribution with shape α and…

Q: A city in the shape of a rectangle stretches 5 kilo-meters from west to east and 3 kilometers from…

A: The problem is asking us to find the expected distance covered by the helicopter in travelling to a…

Q: The position and elevation of a survey station are given by the random vector x= x, in |X3 which X,…

A: Hi, there! since, the multiple questions are posted, we are allowing solving first question. Kindly…

Q: a) The Determine and time B estimate: Activity A C also estimates. the find expected to 6 5 of time…

A: Given information: A B C 10 6 5 12 8 10 14 12 12

Q: EZ = X +Y if X,Y are

A: X follows normal distribution with mean 0 and variance 1. Y follows normal distribution with mean 0…

Q: Q3. Suppose that X¡, i = 1,2, ...,n have an Exponential distribution with parameter a. a) Find…

A: Introduction :- Here the random variable follows exponential distribution with parameter lambda. We…

Q: ssume that females have pulse rates that are normally distributed with a mean of μ=72.0 beats per…

A: Given that The females have pulse rates that are normally distributed . Mean (μ) = 72 beats per…

Q: Products A and B have the same daily demand distribution; Normal with mean 200 and standard…

A: Solution: Given information: The daily demand distribution of producr A and B are normal with given…

Q: An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

Q: Assume that females have pulse rates that are normally distributed with a mean of u = 76.0 beats per…

A: Given information- Population mean, µ = 76 beats per minute Population standard deviation, σ = 12.5…

Q: The first method of moments equation uses the first sample moment about the mean a. True b. False

A: In general, the first method of moment equation uses the first sample moment about the origin.

Q: A random variable X has density 3x2 for 0 < x < 1. Find its variance. (use a decimal number,…

A: Given,f(x)=3x2 ; 0<x<1

Q: a) X is a normally distributed variable with mean u = 30 and standard deviation o = 4. Find i) P(x…

Q: Assume that females have pulse rates that are normally distributed with a mean of μ=72.0 beats per…

Q: This is a Statistics problem. Are the random variables Z1+Z2 and Z1-Z2 the same? Do they have the…

Question

Consider that a ball is thrown with a random angle ? ∈[0,360) (in degrees) and a random
radius ?∈[0,1] (in meters) both independent and uniform. Calculate the density of the
variables ? and ? (the cartesian coordinates of the point at angle ? and radius ?) as well as their
expectation and variance

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Trending now

This is a popular solution!

Step by step

Solved in 6 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

The built-in UKgas data set is a time series of UK gas consumption from 1960Q1 to 1986Q4, in millions of therms. We can easily convert this data to a vector with the assignment x 325. We will reject Ho if z = n) Continuing from part m, what is the value of z? o) Continuing from parts m and n, what is the p value of the test. p) Copy your R script for the above into the text box here. 108 >zstar where s is the sample standard deviation. What is the value of zstar? (Calculate from normal distribution)
The built-in data set, rock, is a data frame recording the measurements of rock sample from a petroleum reservoir. We are interested in the area column of rock. Using R we can convert this column into the vector x by the assignment x30 we can create a confidence interval for μ using a normal critical value. If we want the confidence interval to be at the 94% level and we use a normal critical value, then what critical value should we use? i) Calculate a 94% confidence interval(using a normal critical value) for μ.
The length (in mm) of a spring subjected to a force FNewtons is of the form L = a + BF+ ɛ, where ɛ is assumed normally distributed with mean 0, variance o2. Given the sample statisticsn=D13, E F;= 138, E L; = 577, SEL = -43, SEF= 1735, estimate the expected length of the spring when a force of 11.2 Newtons is applied. (Give your answer correct to 2 decimal places.) Answer: Ti Check 江一 prime viden Type here to search 19 hp ins prt fu f12 f8 f9 f10 f7 f5 f6 『米 " JOI JDI & 6 7 8 5 96 %24 3
A variable of two populations has a mean of 49 and a standard deviation of 14 for one of the populations and a mean of 54 and a standard deviation of 15 for the other population. a) For independent samples of sizes 34 and 45, respectively, find the mean and standard deviation of ₁ - 2. mean: standard deviation: b) Can you conclude that the variable 1 T2 is approximately normally distributed? (Answer yes or no) answer:
Psi is a measure of compressive strength, or the ability of the material to carry loads and handle compression. The desired concrete psi rating used for sidewalks and residential driveways ranges from 2500psi to 3000psi obtained from mixing cement, stone, and sand in different ratios but with the same amount of water. The summary of the psi's of three (3) such concrete mixes made by three (3) different civil engineering students is given as follows: Mean vector: The variance-covariance matrix: Concrete mix Mean Concrete mix 1 Concrete mix 2 Concrete mix 3 Concrete mix 1 | Concrete mix 2 2700 18 12 2 3000 12 16 3 2400 Concrete mix 3 16 25 Let the random variable Y be the vector of the psi's of concrete mixes obtained by the students, i.e. Y1, denotes the psi of concrete mix made by student 1, Y2 is the psi of concrete mix made by student 2 and Y3 is the psi of concrete mix psi made by student 3. (a) Find (i) the multivariate probability distribution function (pdf) of Y. (ii) the…
2
The total expenses of a hospital (dependent variable) are related to many factors. One of these factors is the number of admissions to the hospital (independent variable). Using the summary output below to answer, what is the meaning (analysis) of the coefficient of determination? SUMMARY OUTPUT Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Statistics Regression Residual Total df 0.98706 0.974288 0.972145 8.106794 Coefficients 14 1 12 13 SS 29883.07 788.6412 30671.71 Standard Error Intercept 1.518053 Admissions 0.668591 OA) is the value of Expenses with one unit increase in Admissions 3.248929 0.031354 MS 29883.07 65.7201 t Stat 0.467247 21.32375 F 454.7022 P-value 0.648693 6.59E-11 Significance F 6.59E-11 Lower 95% -5.56075 0.600276 Upper 95% 8.59686 0.736907
3 help
Show full answers and steps to this exercise
Give neat and clean explanation Don't copy from available solutions, I will rate your answer good