Explanation needed! ASAP Let F and G be two cumulative distribution func-tions on the real line. Show that if F and G have no common points ofdiscontinuity in the interval [a, b], then/G(x)dF(x) = F(b)G(b) – F(a)G(a) – / ..(a,b]F(x)dG(x).

The given problem involves the comparison of two cumulative distribution functions (CDFs), F and G,…

Answered: Let F and G be two cumulative…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 68E

See similar textbooks

Similar questions

LetX1,X2,...,Xn be a sequence of independent and identically distributed random variables having the Exponential(λ) distribution,λ >0, fXi(x) ={λe−λx, x >0 0, otherwise Define the random variable Y=X1+X2+···+Xn. Find E(Y),Var(Y)and the moment generating function ofY.
If F(x1, x2, x3) is the value of the joint distribution function of X1, X2, and X3 at (x1, x2, x3), show that the joint marginal distribution function of X1 and X3 is given by M(x1, x3) = F(x1, q, x3) for −q < x1 < q, −q < x3 < q and that the marginal distribution function of X1 is given by G(x1) = F(x1, q, q) for −q < x1 < q With reference to Example 19, use these results to find (a) the joint marginal distribution function of X1 and X3; (b) the marginal distribution function of X1.
Let X be the number of microorganisms in a proliferation culture whose Function of Cumulative Distribution (fda) is given by: F(x) = 1 − e−λx, for x > 0. What is the value of λ such that P(X ≥ 10.14) = 0.8
Let X1,X2,... be a sequence of identically distributed random variables with E|X1|<∞ and let Yn = n−1max1≤i≤n|Xi|. Show that limnE(Yn) = 0
LetX1,X2,...,Xn be a sequence of independent and identically distributed random variables having the Exponential(λ) distribution,λ >0, fXi(x) ={λe−λx, x >0 0, otherwise (a) Show that the moment generating function mX(s) :=E(esX) =λ/(λ−s) for s< λ;
f(x), a continuous probability function, is equal to 1 , and the function is restricted to 0 ≤ x ≤ 12. What is P (0 < x <12)?
Let X ∼ Unif(0, 2) and Y ∼ Bi(2, 0.5). If Z is a mixture of X and Ywith equal weights, graph the cumulative distribution function of Z, andfind Var(Z).
Find the moment-generating function of the continuous random variable X whose probability density is given by f(x) = 1 for 0 < x < 1 0 elsewhere and use it to find μ’1,μ’2, and σ^2.
Let p(x) = cx^2 for the integers 1, 2, and 3 and 0 otherwise. What value must c be in order for p(x) to be a legitimate probability mass function?
f(x) for a continuous probability function is 1/18 , and the function is restricted to 2 ≤ x ≤ 20. What is P(x < 2)?
X1 and X2 are two discrete random variables, while the X1 random variable takes the values x1 = 1, x1 = 2 and x1 = 3, while the X2 random variable takes the values x2 = 10, x2 = 20 and x2 = 30. The combined probability mass function of the random variables X1 and X2 (pX1, X2 (x1, x2)) is given in the table below a) Find the marginal probability mass function (pX1 (X1)) of the random variable X1.b) Find the marginal probability mass function (pX2 (X2)) of the random variable X2.c) Find the expected value of the random variable X1.d) Find the expected value of the random variable X2.e) Find the variance of the random variable X1.f) Find the variance of the random variable X2.g) pX1 | X2 (x1 | x2 = 10) Find the mass function of the given conditional probability.h) pX2 | X1 (x2 | x1 = 2) Find the mass function of the given conditional probability.i) Are the random variables X1 and X2 independent? Show it. The combined probability mass function of the random variables X1 and X2 is below
1. Let f (x) = cx 3 and S X = [0, 2] (X is continuous and c is a constant) a. Find the expectation of X, E(X).b. What is P (0.5 < X < 1.5)?c. What is P (0.5 < X < 2.5)?

SEE MORE QUESTIONS

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

SEE MORE TEXTBOOKS

Let F and G be two cumulative distribution func- tions on the real line. Show that if F and G have no common points of discontinuity in the interval [a, b], then - |G(z)dF (2) = F(b)G(b) – F(a)G(a) – F(x)dG(x). (a,b]