IF x is distributed as a continuousuniform distribution over the interval(ab) prove that- the Median of this distributionis equal to it's Mean

Here's the proof that for a continuous uniform distribution over an interval (a, b), the median (M)…

Answered: IF x is distributed as a continuous…

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 lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is more than 50.5 min. P(X > 50.5) = (Report answer accurate to 2 decimal places.)
) Determine the mean (μ!" ) of sample means distribution (x#-distribution).b) Determine the standard deviation (standard error) (σ!" ) of sample means distribution(x#-distribution).c) Draw a Normal (bell-shaped) graph for sample means distribution (x#-distribution) byhand on a paper showing x and y axes without any values marked on them. However,label the values of mean and standard deviation as described below. The adult male heights in a country vary normally with mean of 70 inches and standarddeviation of 4 inches. We draw many samples of size 100 from the above populationusing repeated random sampling and record the mean height for each sample to constitutea sample means distribution (x#-distribution). Do the above for the distribution.
The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is more than 51.4 min.P(X > 51.4) = (Report answer accurate to 2 decimal places.)
The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is less than 50.6 min. P(X < 50.6) = (Report answer accurate to 2 decimal places.)
The time (in minutes) it takes Greg to complete a homework problem is uniformly distributed (continuously) on the interval (15, 28). What is the standard deviation of the time it takes to complete a homework problem?
Let X be b(2, p) (binomial distribution). Assume P(X > 1) = (a) Find p. (b) Compute P[X = 2]. %3D
Suppose the time it takes my daugther, Lizzie, to eat an apple is uniformly distributed between 6 and 12 minutes. Let X = the time, in minutes, it takes Lizzie to eat an apple. What is the distribution of X? X ~ (,) Please show the following answers to 4 decimal places. What is the probability that it takes Lizzie less than 5 minutes to finish the next apple? What is the probability that it takes Lizzie more than 10.6 minutes to finish the next apple?
The lengths of a professor's classes has a continuous uniform distribution between 49.2 min and 55.5 min. If one such class is randomly selected, find the probability that the class length is more than 52.1 min. P(X > 52.1) = (Report answer accurate to 4 decimal places.)
Suppose the random variable X has a continuous uniform distribution on the interval (20,80). What is P(X > 52 | X > 28)? (Give your response to at least 3 decimal places
The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is more than 50.5 min.P(X > 50.5) = (Report answer accurate to 2 decimal places.)
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 265 feet and a standard deviation of 40 feet. Let X be the distance in feet for a fly ball.a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly hit fly ball travels less than 264 feet. Round to 4 decimal places.
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 275 feet and a standard deviation of 35 feet. Let X be the distance in feet for a fly ball. a. What is the distribution of X? X ~ N(,) b. Find the probability that a randomly hit fly ball travels less than 265 feet. Round to 4 decimal places.

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IF x is distributed as a continuous uniform distribution over the interval (ab) prove that - the Median of this distribution is equal to it's Mean