The distribution function ‘F’ is given by F(x) = 0, x < 0 ½, 0 ≤ x <1 3/5, 1 ≤ x < 2 4/5, 2 ≤ x < 3 9/10, 3 ≤ x < 3.5 1, x ≥ 3.5 a) Calculate the probability function of x, P(x) b) Sketch P(x) and F(x)

The distribution function ‘F’ is given by F(x) = 0, x < 0 ½, 0 ≤ x <1 3/5, 1 ≤ x < 2 4/5, 2 ≤ x < 3 9/10, 3 ≤ x < 3.5 1, x ≥ 3.5 a) Calculate the probability function of x, P(x) b) Sketch P(x) and F(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: Let X and Y be independent v.a with uniform distribution on the interval (0, 20) and (0, 30)…

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: Assume that X has the distribution N (10, 4), find: P (Z > - 3) P (11.36 < X < 16)

A: From the provided information, Mean (µ) = 10 Standard deviation (σ) = 4 X~N (10, 4)

Q: The projection X of the radius-vector of a random point on a circumference of radius a onto the…

Q: What is the definition of the entropy H(X) of a probability space (X, p)

Q: Suppose f(x,y) = ry for 0<x<2, 0<y<2 then the mariginal probability distribution of X is 4

A: The marginal probability distribution formula of X is:

Q: Suppose the joint probability distribution of X and Y is given by f(x,y)= parts (a) through (d). (a)…

A: X=3 X=4 X=5 X=6 Total Y=4 7114 8114 9114 10114 34114 Y=5 8114 9114 10114 11114 38114…

Q: Suppose the joint probability distribution of X and Y is given by f(x,y) = x+y , for x 2, 3, 4, 5; y…

Q: If the joint distribution function of X and Y is given by F(x,y)=1-e* -e +e**); x, y>0. Are X and Y…

Q: The Joint P.D.F. of X and Y is given by f(x,y)-(3-x-y (3-x-y.0<x<1, 0<y<1 0, otherwise a) Find…

Q: Assume that X is uniformly distributed on the set S = {- 3, -2, -1,0,1,2,3}, that is, X assumes each…

A: Firstly list down the possible elements of y variable where The set Y is obtained as: Hence the…

Q: Let X has uniform distribution on [-1,1]. Find E(X|X²).

A: Given: X has uniform distribution on [-1,1]. Then the pdf is: f (x)=12for -1<X<10Otherwise

Q: b) Let X be the random variable with the cumulative probability distribution: 0, x < 0 W F(x) = kx²,…

Q: Suppose that P is a probability measure defined on the sample space S. Prove that P(AOB")=1-P(A)–…

A: Solution: 3. It is needed to prove that

Q: 01: If the random variable (x) has a uniform distribution on the interval [0,6]. Find: a) P(1 < x <…

Q: 3. Let X be a random variable with distribution function P(X ≤x} = { 0 x 1 if x ≤ 0, if 0 1. Let F…

Q: Consider the following function given below with a specified range for the variable t, where t…

A: Given, the probability density function of the time required to clear a minor traffic accident on a…

Q: The continuous random variable X has probability density function (pdf) 1 fx(x) 20 - 0 x).

A: "Hello. Since your question has multiple parts, we will the solve first question for you. If you…

Q: If the distribution function of X is given by for x <2 for 2sx<3 36 for 3sx<4 for 4sx <5 36 for 5 sx…

A: A discrete random variable has only discrete values which can be counted. For example a random…

Q: Verify that the following is a distribution function:

Q: 2) Required probability is given by 99 P(X 2 100) = 1 - (C")-0.01°- 0.99-3 = 1 - 0.0092427 0.990757…

A: Here the given probability calculation is given :

Q: Q4-Find the distribution function associated with f(x) = , for 0 < x < 1 or 2 < x < 4, and zero…

Q: 2. Consider the function Fx(x) = 0 E. x 2. (a) State the 4 properties of a distribution function.

A: Given: FX(x)= 0 x<0=x2…

Q: Which of the following represents the two properties a continuous probability distribution must…

A: Given, The properties of distribution function and probability density function.

Q: What is the probability P (X> 3) if there is a continuous probability distribution with f (x) = cx…

A: We have to find given probability..

Q: Calculate the probability that is between 0.2 and 0.7, if x is uifomly distributed in the interval…

Q: -(0.298x+0.596) Find c such that the function f(x)= ace range x>0.812. Select one: O a. 0.59104815 O…

A: Given the function want to find the value of such a given function is a probability distribution…

Q: = cx and 0<X <4, dd: 0 is a continuous probability distribution, * which of the following options is…

A: We have to find correct answer from given options...

Q: 11. The probability distribution function, P(X-x) of a discrete random variable X is defined as for…

A: Part a: We have been given the probability distribution function as, P(X=x)=27 for x=047…

Q: Let x1 ~ N(0,1), X2 ~N(-1,4) and X3~N(1,9) be independent. Derive the distribution of Y=x1-x2-2x3…

A: Normal Distribution: A continuous random variable X is said to follow Normal distribution with…

Q: If the joint probability distribution of X and Y is given by * f (x, y) x+y for x = 0,1,2,3; y =…

Q: Show that the Cauchy probability distribution does not have the first moment that is, E(X) does not…

A: The objective is to show the first moment does not exist for cauchy distribution

Q: Suppose that you enter a fantasy basketball league. Suppose that the 2022 team budget, say X, is…

A: The pdf of a uniform distribution on [a, b], when a and b are the minimum and maximum values,…

Q: 0. Let st have the distrobution of X ~N (4,16). (a). P(x >xo) = 0.05, (b). Fmd the number Xo smce…

A: Here it is given that X~N(4,16). We need to find the value of X0 for the two given conditions.

Q: 2) Let X & Y have the joint probability function f(x,y) = cx²y, -y ≤ x ≤ 1,0 ≤ y ≤ 1. i) Find c such…

A: Let X and Y have the joint probability function f(x,y)=cx2y ; -y≤x≤1, 0≤y≤1 0 ; otherwise

Q: Let X represent a continuous random variable with a Uniform distribution over the interval from 0 to…

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…

Question

The distribution function ‘F’ is given by
F(x) = 0, x < 0
½, 0 ≤ x <1
3/5, 1 ≤ x < 2
4/5, 2 ≤ x < 3
9/10, 3 ≤ x < 3.5
1, x ≥ 3.5
a) Calculate the probability function of x, P(x)
b) Sketch P(x) and F(x)

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

When a man observed a sobriety checkpoint conducted by a police department, he saw 656 drivers were screened and 5 were arrested for driving while intoxicated. Based on those results, we can estimate that P(W)equals=0.00762,where W denotes the event of screening a driver and getting someone who is intoxicated. What does P(W) denote, and what is its value? What does P(W) represent? P(W)=
Prof that' For a fixed B with P(B) > 0, P(A l B) is probability function.
Let f(x) = x for 0 < x < 1. Is f(x) a legitimate probability distribution function (pdf) for a continuous random variable? No, the area under f(x) is not 1 (it is greater than 1). Yes, all criteria for a pdf are satisfied. No, the area under f(x) is not 1 (it it less than 1). No, f(x) is not non-negative.
Assume that X is a random variable whose conditional distribution given the variable Y is poisson P (X | Y) = Po (Y). Suppose further that Y has a gamma distribution Y ∼ Gamma (1, 1). (a) Determine the value E (XY). (b) Determine the conditional distribution P (Y | X).
The amount of time it takes Susan to wait for the bus is continuous and uniformly distributed between 4 minutes and 18minutes. What is the probability that it takes Susan less than 5 minutes given that it takes less than 11 minutes for her to wait for the bus
poisson distribution
i need the answer quickly
Let X have a uniform distribution on the interval (2, 9). Find the probability that the sum of 2 independent observations of X is greater than 16.
c) Suppose that a random variable Y is uniformly distributed on an interval (0,1) and let c> 0 be a constant. i) Find the moment generating function of X = -cY. ii) What is the distribution of X? 2| Page
Question 2: X ~ Geometric(T) distribution with probability function p(x) = P(X = x) = T(1 – 7)"-1 for x = 1, 2, 3, ... Find P(X x).
Let Y1, Y2,., Ya be a collection of independent random variables with distribution function y 8 Show that Y converges in probability to a constant, and provide that constant. 1
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