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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![Q1:Show that: If X1, X2, , Xn are independent random variables and
X = X1 + X2 ++Xn, 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)?
1
Chapter 3
Let X be a discrete random variable with range Rx = {1, 2, 3, ...}.
Q4:
Suppose the PMF of X is given by
1
for k = 1, 2, 3, ...
2k
Px (k) =
a) Find and plot the CDF of X, Fx (a).
b) Find P(1 < X < 3).
Chapter 3
Functions of Random Variables
Q5: Example. Let Rx = {0,
T T 37
, such that
4'2
4.
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 three
item 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.
3
Chapter 3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e3ff238-ba1d-4e08-8bd7-040d3bc800b6%2Fc9ba4d57-4be0-4e45-9ff7-e5d6a11d92e2%2F7rvo9c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q1:Show that: If X1, X2, , Xn are independent random variables and
X = X1 + X2 ++Xn, 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)?
1
Chapter 3
Let X be a discrete random variable with range Rx = {1, 2, 3, ...}.
Q4:
Suppose the PMF of X is given by
1
for k = 1, 2, 3, ...
2k
Px (k) =
a) Find and plot the CDF of X, Fx (a).
b) Find P(1 < X < 3).
Chapter 3
Functions of Random Variables
Q5: Example. Let Rx = {0,
T T 37
, such that
4'2
4.
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 three
item 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.
3
Chapter 3
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