3. Draw the cumulative distribution functions of the following distributions:(a) A continuous random variable chosen uniformly from the interval [1,6].(b) A continuous random variable chosen uniformly from the union [1,2] U [3, 4] U [5,6].(c) A discrete random variable chosen uniformly from the set {1, 2, 3, 4, 5, 6}.

Let X be a continuous uniform distribution Ua,b, then the probability density function of X is given…

Answered: Draw the cumulative distribution…

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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Similar questions

The continuous random variable X has a U (-6, 6) distribution, i.e. uniformly distributed between the points a = -6 and b = 6. What is the mean of X, and what is P (-3 < X < 1)?
let X(n,p) denotes binomial random variable with parameters n and p. Show that X(n+1,p) >st ( greater than equal ) X(n,p)
Prove a formula for the moment-generating function (mgf) of Y in terms of the mgf's of X₁ and N. For any random variable Z, the mgf is defined as oz(s) = E[e³Z], where s € IR and whenever the expectation is defined.
3. Draw the cumulative distribution functions of the following distributions: (a) A continuous random variable chosen uniformly from the interval [1,6]. (b) A continuous random variable chosen uniformly from the union [1,2] U [3, 4] U [5, 6]. (c) A discrete random variable chosen uniformly from the set {1, 2, 3, 4, 5, 6}.
b) calculate var(x) Give your answer to four decimal places.
Let (Ω, Pr) be a probability space, and let X and Y be two independent random variables that are positive and have non-zero variance. (a) Prove that X^2 and Y are independent. Note that by symmetry, it will also follow that Y^2 and X are independent. (b) Use the result from part (a) to show that the random variables W = X + Y and Z = XY are positively correlated (i.e. Cov(W, Z) > 0).
Let X(1), X(2), ..., X(n) be the order statistics of a set of n independent uniform (0, 1) random variables.Find the conditional distribution of X(n) given that X(1) = s(1), X(2) = s(2), ..., X(n-1)=s(n-1).
Let X1 and X2 be two independent and identically distributed random variables with N(µ, 1) distribution. Calculate the conditional distribution X1 | {X1 + X2 = s}.
Let X₁, X₂, ..., X5 be a random sample from N(1,4) and let Y₁, Y₂, Y3 be an independent random sample from N(3, 4). Find P > 1) using a proper F distribution, where S and S are sample variances for the two random samples respectively. In R/RStudio, the function of can be used for compute the probabilities based on F distribution.

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