Consider a random variable X with possible outcome:0,1,2...... Suppose that P(X=j) = (1-a)a^j, j=0,1,2,..... 1) for what value of a is the above model meaningful? 2) Verify that the above does represent a legitimate probability distribution. 3) obtain cumulative distribution function of X.

Consider a random variable X with possible outcome:0,1,2...... Suppose that P(X=j) = (1-a)a^j, j=0,1,2,..... 1) for what value of a is the above model meaningful? 2) Verify that the above does represent a legitimate probability distribution. 3) obtain cumulative distribution function of 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: Question 1. Let X and Y be independent random variables. Suppose that the moment generating…

Q: a) Show that the following function is a valid probability mass function of the random variable X.…

A: For each probability mass function, There are two conditions to satisfy 1 : f(x) >=0 for all S…

Q: (b) Let a discrete random variable X have the following PMF: p(x) = k (=) , for x = 1,2, . ..; 0,…

A: Basic probability

Q: Suppose that the random variables X, Y, and Z have the following joint probability distribution…

A: d) To find the expected value (mean) of Y, we can use the formula: E(Y) = Σ y * P(Y = y), where the…

Q: In a class of 8 students, what is the probability that at least one was born in July?

A: c) Given that there are 12 months in a year. The probability that student born in July is…

Q: Exercise 3. Let X be a random variable with mean and variance o2. For a ER, consider the expectation…

A: Given information: The random variable is X. The mean of X is μ. The variance of X is σ2. The term a…

Q: Q.2) (a) Show that the following function satisfies the properties of a joint probability mass…

A: The joint probability mass function of random variables (X,Y) is given as:xy111.521.532.5435

Q: Q1: If the value of the joint probability distribution of X and Y are as shown in the table: a) What…

Q: variables X and Y. Using this information answer the questions below. Y=2 4c 2c X=1 X=2 That is, P(X…

Q: Let X be a random variable with p.d.f. 0<x<0 S(x) = • ,find E(e3) O.w

A: Hey there! Thank you for posting the question. Since there are multiple questions posted, we will…

Q: Let X be the random variable, and create two new copies of this X₁, X₂ ~X x | P(X = x) 0 0.5 1 0.2 2…

A: To determine whether 2X and X1 + X2 have the same distribution, we need to compute their respective…

Q: The probability distribution of random variable X is a) b) c) d) Show that k = 6. Find P(X <3). P(X=…

A: Hi! Thank you for the question. As per the honor code, we are allowed to answer three sub-parts at a…

Q: Let P(x) = , x = 0,1, 2,3 be a probability distribution for a discrete random variable X, find: %3D…

Q: Suppose X is a random variable and suppose the possible values that it can assume are given by a, b,…

A: Given, X is a random variable

Q: ) Let X and Y be two discrete random variables. Their joint probability mass function is as follow…

Q: The amount of time an air-conditioning technician to repair a unit is in between 1.9 and 5 hours…

Q: Show that the following function is a valid probability mass function of the random variable X. p(x)…

A: Each probability mass function p(x) satisfies following two conditions: p(x)>=0, for all…

Q: 2. 2 For the random variable Y with pdf f-V)-+v.os y s1,0 else, (a) Find the expectation E(Y) and…

A: The probability density function (PDF) for a random variable gives the probability at each possible…

Q: et Y₁, Y2, ..., Yn be a random sample whose probability density function is given by 0 0 elsewhere…

Q: Let the random variables X₁, X₂ be independent of each other, well and obey the same geometric…

Q: A delivery truck travels from point A to point B and back using the same route each day. There are…

A: a. P(x1 + x2 = 4 ) = P(0,4) + P(1,3) + P(2,2) + P(3,1) + P(4,0) = 0.01+0.03+0.15+0.07+0.01…

Q: X is a discrete random variable with p.m.f given by P(X=x)= x/c where c is a constant. The support…

Q: B4 Let X,,X,..,X„ be a random sample from the exponential distribution with mean e, and let…

Q: Let X and Y have a bivaraite gamma distribution of Kibble with parameters a = 1 and 0<0< 1. What is…

Q: i) Find the conditional distribution of the likelihood function given the function of the statistic,…

Q: If X is a continuous random variable that takes on values between 10 and 40, then the P(X = 15.5) =…

A: We have given that X is a continuous random variable that takes on values between 10 and 40, then…

Q: for x = 1, 2 and y = 1, 2, 3, 4 2. Suppose f (x, y) = { 50 To. elswhere a) Show that f(x, y) is a…

A: Given: The joint density function is as follows fx,y=x2 ×y50 x = 1,2 y = 1, 2, 3, 4

Q: Let X be a random variable with p.d.f f(x): mode. x = 1,2,3, ... .Find the O 2,4 O 1.3 O 1,2 2,3

Q: A discrete random variable has the p.mf f(x) = ax x=1, 3, 5 O A. 0.11 O B. 9 OC. 4.5 O D. 5

A: Given data: f(x) = a.x Where , x = 1,2,3 To find : value of a

Q: 4. Determine the values of c so that the following functions represent joint probability…

A: The question is about joint probability distribution.Given :

Q: 4. Determine the values of c so that the following functions represent joint probability…

A: The objective is to find the value of by representing each function as a joint probability…

Q: TABLE 13-6 Let X and Y be two random variables each X -1 ! luking three values -1, 0 and 1, and…

Q: If X and Y are both random variables with a joint probability distribution: Se-(z + y), r > 0, y >…

Q: Suppose R is a discrete random variable that only takes positive integer values. Suppose the…

A: Introduction: The cumulative distribution function (cdf), of a discrete random variable, X is given…

Q: Exercise 4 Suppose X and Y are independent random variables such that X has uniform (0, 1)…

Q: Which of the following are a valid probability function for the given random variable? Select all…

A: Solution Here the valid probability function identified if sum of all f(x) =1 where x are values of…

Question

Consider a random variable X with possible outcome:0,1,2...... Suppose that P(X=j) = (1-a)a^j, j=0,1,2,.....

1) for what value of a is the above model meaningful?

2) Verify that the above does represent a legitimate probability distribution.

3) obtain cumulative distribution function of X.

4) show that for any two positive Integers s and t, P(X > s + t | X > s )= P X is great than equal to t).

Video Video

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

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Suppose that a discrete random variable X has a distribution with the following probability (4cx,x = 2,3,5 ( 0, otherwise function: f(x) a. Determine the value of the constant c: b. Calculate Pr (X > 3) (please use the value of c from part a.):
1. The random variables §, §1, §2,... are independent and identically distributed with 1/4 and P(§ = j) = c/j for j = 1,2,3. Let X₁ = 0 and Xn = max(§₁, ..., Èn) for n = 1, 2,.... distribution P(§ = 0) = (a) What value must c take? (b) Explain why {Xn, n = 0, 1, 2,...} is a Markov chain. (c) Write down the transition matrix. (d) Draw the transition diagram and classify the states (aperiodic, transient, re- current, eorgodic, etc). (e) Calculate P(Xn = 0). (f) Calculate P(X₁ = 3, X₂ = 1|X₁ = 3).
Correction: 1b) What is E?
1.STATISTICAL INFERENCE
Let X and Y be two discrete random variables with the joint probability distribution is given by: Y= f(x.y) 2 1/6 1/3 1/12 X= 1/6 1/12 2 0 1/6 Then E ([(X + 2Y)®]) is equal to: None of these 147/12 57/6 281/12
What is the expected value of U?
Let X; (i = 1, 2,..., n) be i.i.d. exponential random variables with E{X;} = 1/A. Let Y = mn{X1, X2,..., Xn}. What is the distribution of Y? (Compute P{Y > y}.) What is the distribution of Z = max{X1, X2, ..., Xn}? (Compute P{Z < z}.)
Is P(S = s) = fs(s) = 1+11+1 ; s = 0,1,2,... 0; е. w. a discrete probability function? Why or why not?
The probability generating function for a random variable X is given by: 9x(z) = 1 1 10. 1 I 20 8 -25 + 4 P(X > 10 |X < 22) equals Select one: a. 0.286 b. 0 c. 0.8 d. 1 е. 0.2
3. Determine the value c so that each of the following functions can serve as probability distributions of the discrete random variable X: a. f(x) = c(x² +4) for x = 0,1, 2, 3; 3 b. f(x)%3Dс for x= 0,1, 2 3-x
3 Let X be a random variable with probability Law P (X = r) = q, K for r = 1,2,3.. . 00, Find the moment generating function and mean of ihe random variable X. Let K+ q = 1.