Q1:Show that: If X1, X2, , Xn are independent random variables andX = X1 + X2 ++Xn, thenQ2: What is the expectation and the variance of RV X, where X represents the out come throwing a die?Q3: Find the expectation and the variance of X, where X is binomial random variableX - Binomial (n, p), Var(X)?1Chapter 3Let X be a discrete random variable with range Rx = {1, 2, 3, ...}.Q4:Suppose the PMF of X is given by1for k = 1, 2, 3, ...2kPx (k) =a) Find and plot the CDF of X, Fx (a).b) Find P(1 < X < 3).Chapter 3Functions of Random VariablesQ5: Example. Let Rx = {0,T T 37, such that4'24.Find E[sin(X)].Q6: A machine produces a defected items with a probability of 0.1. What is the probability that in a sample of threeitem will have at most one item defected?Q7: For any independent X, and Y random variables, E[XY]=E[X]E[Y]. Show that?Q8: Suppose RV X has the following PMF: p(0)=0.2, p(1)=0.5, p(2)=0.3. Find E[X], E[X^2], E[X]^2.3Chapter 3

Note: As per bartleby guidelines for more than one questions asked, only one question is to be…

Q1:Show that: If X1, X2, ., X, are independent random variables and X = X1 + X2 +….+ X, , then Q2: What is the expectation and the variance of RV X, where X represents the out come throwing a die? Q3: Find the expectation and the variance of X, where X is binomial random variable X - Binomial(n, p), Var(X)?

Q1:Show that: If X1, X2, ., X, are independent random variables and X = X1 + X2 +….+ X, , then Q2: What is the expectation and the variance of RV X, where X represents the out come throwing a die? Q3: Find the expectation and the variance of X, where X is binomial random variable X - Binomial(n, p), Var(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...

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