A uniform distribution is a continuous probability distribution where every valueof X on an interval is equally likely to be the outcome.If X is defined on the interval [a,b], then when graphed the density function forthe distribution will be a horizontal line of height with domain [a,b].Probabilities on a continuous random variable can be determined by calculatingthe area under the curve of the graph of the density function for the distribution.In general: For a uniform distribution function defined on [a,b]P(X < c) =P(X> c)=b-ab-cb-aP(c < X < d) =d-cb-awhere c 6.2)

From the provided information, X is random variable with a uniform distribution for 5 < X <…

Answered: A uniform distribution is a continuous…

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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Suppose that X, .., X, is an independent and identically distributed sample from some distribution family G defined by an unknown parameter value 0. Also suppose that the posterior distribution for 0 has the probability density function p(0|x1,...Xn). The Bayes estimator for 0 is the expected value of the posterior distribution, i.e. E[0]x1, .., Xn]. True False
OQuestion 1: Continuous random variables – Uniform distribution Suppose that X = The thickness of a conference-hall wall in cm, is a continuous random variable with a uniform distribution on [A, B]. a) Find the cumulative distribution function if A=12 cm and B=18 cm. b) What is the probability that wall thickness exceeds 14 cm? c) What is the probability that the wall thickness is between 13 cm and 16 cm? d) What is the expected wall thickness if A = 12 cm and B= 18 cm? e) Describe by words what is the shape of the area under the density curve of the thickness of the conference-hall wall.
A motorcycle drives from Welcome Rotonda to Fairview and back using the same course everyday. There are four stoplights on the course.Let x denote the number of red lights the motorcycle encounters going from Welcome Rotonda to Fairview and y denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (x, y) is given by 2 3 0.07 0.01 0.05 0.01 0.03 0.01 0.03 0.08 0.03 0.02 2 0.03 0.11 0.15 0.01 0.01 3 0.02 0.07 0.1 0.03 0.01 4 0.01 0.06 0.03 0.01 0.01 Find: 1. Standard deviation of Y. 2. Fill in the blanks As the number of motorcycle drivers from Welcome Rotonda to Fairview encountered by the motorcycle (increase, decrease, or be (zero, negative, or positive) covariance. The increases, the number of stoplights of its return trip tends to uncorrelated). Therefore, X and Y have a covariance was calculated to be (numerical value). *Describe the correlation whether a strong, a weak, or no. X and Y have correlation.…
The posterior distribution for the random variable e Select one: a. f(x\e) h(e\x) = g(x) b. T(e)f(x\e) g(x) h(e\x) = C. f(x\e) T(e)g(x) h(e\x) = d. g(x)f(x\e) h(e\x) =
Suppose that we have an independent and identically distributed sample from some distribution family G defined by an unknown parameter value 0. The frequentist approach to statistics would treat e as a fixed value (constant), but the Bayesian approach to statistics would treat 0 as a random variable with some prior distribution specified by a probability density function 1(0). True O False
Let X be a random variable whose probability density function is plotted below. If one was to generate X by passing a uniform (0, 1) random variable through a function, then what function would you use? (your answer should be a function of x). 0.9- 0.8- 0.7- 0.6- 0.5 qula Snip 0.4 0.3- 0.2- 0.1 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0
Let X denote a random variable having a distribution. If F(x)=ax³ where 0≤x≤(+3). Find f(x) after getting the constant value (a) and find the probability P(2
Let a function of random variable X is given by ( refer pictures) : a) Find the value of K b) Form the table of probability distribution of X C) Find the mean and variance of the distribution
A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 50.0 and 52.0 minutes. Find the probability that a given class period runs between 50.75 and 51.5 minutes. Find the probability of selecting a class that runs between 50.75 and 51.5minutes.
A motorcycle drives from Moraytato Lacson and back using the same course everyday. There are four stoplights on the course. Let x denote the number of red lights the motorcycle encounters going from Morayta to Lacson and y denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (x, y) is given by x y 0 1 2 3 4 0 0.01 0.01 0.03 0.07 0.01 1 0.03 0.05 0.08 0.03 0.02 2 0.03 0.11 0.15 0.01 0.01 3 0.02 0.07 0.1 0.03 0.01 4 0.01 0.06 0.03 0.01 0.01 (g) Give the standard deviation of X. Answer=
A motorcycle drives from Welcome Rotonda to Fairview and back using the same course everyday. There are four stoplights on the course. Let x denote the number of red lights the motorcycle encounters going from Welcome Rotonda to Fairview and y denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (x, y) is given by 1 2 4 0.01 0.01 0.03 0.07 0.01 0.03 0.05 0.08 0.15 1 0.03 0.02 2 0.03 0.11 0.01 0.01 3 0.02 0.07 0.1 0.03 0.01 4 0.01 0.06 0.03 0.01 0.01 Find: (a) Give the marginal probability distribution of fx (0). (b) Give the marginal probability distribution of fy (3). (c) Give the conditional density distribution of X=3 given Y = 3. (d) Give E(X). . (e) Give E(Y). (1) Give E(X) Y = 3). (g) Give the standard deviation of Y. *Complete the interpretation of the data. As the number of from Welcome Rotonda to Fairview encountered by the motorcycle increases, the number of stoplights of its return trip tends…
Given the discrete probability distribution shown to the right, a Calculate the oxpected value of x b Calculate the variance of x c Cakculate the standard deviation of x 75 100 125 P(x) O 0.20 0.30 0.50 a E00 =D (Type an integer or a decimal.) bo-O (Type an integer or a decimal) (Type an integer or decimal rounded to two decimal places as needed)

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