8.18. Let X be a binomial random variable with parameters n and p, which meansthat its mass function is given byƒ(1 (*)p²(1–p)**,= (*) p² (1-p)*-*, i=0,...,,and 0 otherwise. Prove thatE1+X=1-(1-p)"+1(n+1)p

binomial distribution is defined as A random variable is said to follow the binomial distribution…

Answered: 8.18. Let X be a binomial random…

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

Similar questions

1.1 Consider Y₁, Y2, ‚Yn are i.i.d. random variables with n > 4 and T is the sample mean Y. Also let W = 1 Y¿. Then (A) E(Y₁ +Y₂|W) = E(Y₁+Y₂) (B) E(W|T) = E(Y₁|T) (C) E(Y₁+W|W) = E(Y3 + Y4|W) (D) none of the above.
11. Let (yı, Y2, .., Yn) be independent random sample from the uniform distribution on [0, 1]. (a) show that Z = – In Y; has exponential distribution with parameter 1. (b) Hence or otherwise, show that –2) In Y; Xản i=1
1. 1. Let X;, i = 1, 2, ..., n be i.i.d. exponential random variables with mean 1. By the Central Limit Theorem, %3D Vn( X;/n – 1) → N(0, 1). i=1 Verify that the Lindeberg condition and the Lyapunov condition are satisfied.
a) Let X₁, X2, ..., X₁ be a random sample of size n from population X. Suppose that X has the following probability mass function: (0(1-0)-¹, f(x; 0) = {0, x = 1,2,3,... elsewhere iii) Show whether or not X, is a consistent estimator of the parameter
Let X1,..., Xn be independent and identically distributed random variables with Var(X1) < ∞. Show that n 1 EjX;→p EX1. п(п + 1) j= Note. A simple way to solve a problem of showing Yn →p a is to establish limn EYn = a and limn Var(Yn) = 0.
2. a. If X is a discrete random variable with probability mass function P(X =x) and a, b are constants, prove that E(aX +b)= aE(X)+b, ii. Var (ax +b)=a³Var(X). i.
None
9. Two discrete random variables X and Y have joint probability mass function (pmf) 1,2,...,n; y = 1, 2, . . . , x. f(x) = { k n(n+1) 0 Xx = otherwise (d) Use the fact that E(Y) = Ex (Ey\x(Y|X)), where Ex( ) and Ey|x( ) are the expected values with respect to X and with respect to Y given X, respectively, to show that E(Y) = n(n+³) 4
11. Let (y1, Y2 ... Yn) be independent random sample from the uniform distribution on [0, 1]. (a) show that Z = – In Y; has exponential distribution with parameter 1. (b) Hence or otherwise, show that -2 In Y; xản
Q1 1. The following spinner was spun 38 times. What is the probability of spinning A 16 times? Insert Image
19
12 The joint pdf of 2 - random variables is X and Y is fxy (x, y) = k (6 - x - y) for 0

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

8.18. Let X be a binomial random variable with parameters n and p, which means that its mass function is given by ƒ(1 (*)p²(1–p)**, = (*) p² (1-p)-i, i=0,...,, and 0 otherwise. Prove that E 1+X = 1-(1-p)"+1 (n+1)p