Consider a continuous random variable X such that P (−1 ≤ X ≤ 1) = 1/2. Can X be characterized by i) Uniform, and ii) Exponential distributions? If yes, ﬁnd the distribution parameters which ensure the required property for X .

Consider a continuous random variable X such that P (−1 ≤ X ≤ 1) = 1/2. Can X be characterized by i) Uniform, and ii) Exponential distributions? If yes, ﬁnd the distribution parameters which ensure the required property for X .

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...

See similar textbooks

Related questions

Q: 3(x+ x³) for Let f(x) = for 0< x < 2, zero otherwise be the pdf for a random variable X. 14 d) Find…

A: Introduction: The median is the value below which, the probability of obtaining an observation is…

Q: Let X1,.X, be a random sample from a uniform (0,0) distribution and let Y = max(X1,..., the coverage…

A: We have a sample X1, X2,....,Xn from uniform distribution. We know that, Y = max(X1, X2,....,Xn) =…

Q: Example . Let the random variable X of the continuous type have the p.d.f. Ax) = 2/x', 1 <x < o,…

Q: Let X be a continuous random variable. Prove Var(X) > 0.

A: Solution:- Given that let X be a continuous random and prove that Var(X) > 0.

Q: If the variance of a poisson variate is 3. Find the probability that X = 0 i) i) ii) 0<x<3 18x<4

Q: Let X be a nonnegative continuous random variable with the pdf f(x). Read the following statements:…

A: Let X be non negative continuous random variable with pdf f(x).

Q: Exercise 23. Let X be a random variable having the uniform distribution on the interval (0,0+ 1), 0…

Q: Let X be a continuous random variable that is normally distributed with mean, µu = 15 and standard…

Q: Find the probability of event {X ≤5.5} for a Gaussian random variable having #x Ox=2. = 3 and

Q: A) Suppose that X is a random variable with if 0 < x < 2 fx(x) = otherwise

A: We have to find the var(x) Using formula Var(x) = E(x^2) - [E(x)]^2

Q: Let X be a discrete random that takes values from the set {-2,0,2} where P(X=x)= { 1/5 if x=-2 3/5…

A: From the given information we want to graph graph of cumulative distribution function.

Q: EXERCISE 3 Let X1, ..., X, be independent exponential random variables with mean 1/ß. Find the…

Q: Suppose that the random variable X has the continuous uniform distribution on the interval [0,1]. A…

A: It is given that X~U(0, 1).

Q: X denotes a binomial random variable with parameters n and p. For each exercise, indicate which area…

Q: The probability mass function of x discrete random variable x = 0, 1, 2, ... is given as p(x) =…

A: Given function is P(x)=(15)(45)x

Q: The random variables x, are i.i.d. and uniform in the interval (-0.5, 0.5). Show that 13 E{(x₁+x2 +…

A: It is given that the random variables X1, X2, X3 are i.i.d and follow Uniform distribution with…

Q: For the continuous probability functionf(x) = Kx when x20 find

Q: Suppose that a random variable X has a hypergeometric distribution with parameters n = 36, N = 50,…

Q: 3. Let X be a random variable that is uniformly distributed on the interval (a, b). Find its moment…

A: Moment Generating Function for a random variable X is given by, E(etX) = ∫-∞∞etxf(x) dx where f(x)…

Q: 16. (BONUS) Use Chebyshev's Theorem to find the following probability. If u = 5, o? = 9. Assume x…

Q: Suppose random variable X has a Poisson distribution with t = 2 and λ= 4. What is E(X)?

Q: Prove that the E(X) = 1/p for a geometric distribution, where x is the number of trials.

A: The geometric distribution with probability that ranges from 0 to 1 is a discrete probability on the…

Q: 3 Let X be a random variable with f(x)= 25x53. 4 0 otherwise a) Find and graph F(x). Find the value…

A: The provided function is, fx=34 0≤x≤114 2≤x≤30 otherwise

Q: fx(x) = (0+1)xº, if 0 ≤ x ≤ 1; otherwise. 0, Find the maximum likelihood estimator of given i.i.d.…

A: X1 are iid r.s.Let random variable X have probability density function

Q: If X is a random variable with Binomial distribution of n=35 and p=0.45, find: i. E(X) ii. Var(X)…

Q: 1. Assume that Z is a standard normal random variable (i.e., it is a normal random variable with…

A: It is an important part of statistics. It is widely used.

Q: A continuous random variable X has the distribution function F(x) = 0 if x 3 The value of k is

A: Given: X has distribution function as : F(X) = 0 if X<1 = k(x-1)^4 if 1<X<3 = 1 if X >3…

Q: If X is a random variable with Binomial distribution of n=35 and p=0.45, find: i. E(X) ii.…

Q: (a) P(2 < Xs 5), (b) P(3 < X s 7), and (c) P(X 2 6). *

Q: (47) Let X b(8, -) find E(5+6x) and distribution function.

Q: Suppose that the random variableX has the continuous uniform distribution í 1,0 < x < 1 0, otherwise…

A: Given that: The probability density function of random variable X is given as: fx=1, 0≤x≤10,…

Q: The continuous random variable T represents the time in hours that students spend on homework. The…

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: If the random Variable x has a uniform distribution the interval [0,5] on Find P(2<XS4).

Q: Example the p.d.f. Ax) = 2/x', 1 < x < ∞, zero elsewhere. The distribution function of X is Let the…

Question

Consider a continuous random variable X such that P (−1 ≤ X ≤ 1) = 1/2.

Can X be characterized by i) Uniform, and ii) Exponential distributions?

If yes, ﬁnd the distribution parameters which ensure the required property for X .

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1: Given information

VIEW

Step 2: Check characteristic of uniform distribution

VIEW

Step 3: Check characteristic of exponential distribution

VIEW

Solution

VIEW

Step by step

Solved in 4 steps with 23 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Assume that x donotes the continuous random varlable with probability distribution of y & (x) and cumulative distribution as ISU FCx) =3x - 2x x>1 What is the P(0.9< X S 2)?
Use TLM method to prove
A random variable X follows a uniform continuous distribution on the range [0, B]. Use mathematical expectation to show the mean is B/2
X denotes a binomial random variable with parameters n and p. For each exercise, indicate which area under the appropriate normal curve would be determined to approximate the specified binomial probability. P(X ≤ 4)
Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
b) calculate var(x) Give your answer to four decimal places.
Find the characteristic function of X² when X has the N(u, o²) distribution.
The distribution of the random variable X is a given by a function:f(x) = 1/c ; 0<x<1, = x/3 ; 1<=x < 2, = 0 ; else Determine the F(x) Count P(X > 1,4)
PLEASE SHOW COMPLETE SOLUTION
X is a normally distributed random variable with mean 72 and standard deviation 22. Use calculator to find the probability indicated. a) P(78<X<127) b) P(60<X<90) c) P(X=80) *continuous
Let X be a continuous random variable that follows a uniform distribution over the interval (-3, 7]. Find the following. a. E(X) b. P(X=6) c. P(X<5) d. P(X|<4)