Consider the sample space {a,b,c,d,e} with probabilities, respectively, .1,.2,.3,.2,.2. Verify that this is a probability space. The random variable X is given by X(a)=1, X(b)=2, X(c)=3. X(d)=4 and X(e)=5. Compute the expected value and variance of X. Let X2 be two iterations of X, addeed, independently. Write down an appropriate probability space for this and compute the expected value and variance of X2 two different ways- directly from the probability space, and also by using our theorems, (If you think of X as the outcome of some game, then X2 is the result of playing the game twice, independently.)

Consider the sample space {a,b,c,d,e} with probabilities, respectively, .1,.2,.3,.2,.2. Verify that this is a probability space. The random variable X is given by X(a)=1, X(b)=2, X(c)=3. X(d)=4 and X(e)=5. Compute the expected value and variance of X. Let X2 be two iterations of X, addeed, independently. Write down an appropriate probability space for this and compute the expected value and variance of X2 two different ways- directly from the probability space, and also by using our theorems, (If you think of X as the outcome of some game, then X2 is the result of playing the game twice, independently.)

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: A motorcycle drives from Buendia to Quiapo and back using the same course everyday. There are four…

A: Note: Hi there! Thank you for posting the question. As there are multiple sub parts, according to…

Q: Let E and F be events of a sample space such that P(E)=0.46, P(F)=0.35 and P(EnF)=0.10. Find the…

A: We have to answer question based on conditional probability.

Q: Assume, North Origano, is a country with highest domestic violence cases (approximately 5 cases per…

A: From the provided information, The probability distribution table is as follow: x f(x) 10…

Q: The number of tails showing when flipping four coins is a discrete random variable. Denote it by X.…

Q: Let X1 ~ N(0,1), X2 ~ N(0,1), and X3 ~ x(n) be mutally independent random variables. Find the…

A: a) If X1, X2,…., Xn are mutually independent normal random variables with mean µ1, µ2,…., µn and…

Q: If the probability function for discrete random variables, X = 1, 2, 5; is P(X) =

A: Given probability function is, PX=18X, X=1,2, 5 X 1 2 5 P(X) 18 28 58

Q: A particular unfair coin is constructed so that the probability of obtaining a tail is 3/4. The…

Q: Suppose that a box contains 9 cameras and that 5 of them are defective. A sample of 2 cameras is…

A: Total number of cameras = 9 Total number of defective cameras = 5 Probability that a camera will be…

Q: Q 5) A die with six faces is rolled. The discrete random variable "X" represents the outcomes on the…

A: given distribution is x 1 2 3 4 5 6 P(X=x) a a a b b 0.3 table represents probability…

Q: Suppose that two coins are tossed. Let x be the number of tails obtained. Calculate the expected…

A: Event: Event is defined as set of outcomes in a statistical experiment. Probability: The probability…

Q: Consider a discrete random variable X that takes values 0, 1, 2, 3, 4, 5, with probabilities 0.1,…

A: The following data has been provided:0123450.10.20.10.30.150.15It is required to calculate the…

Q: The random variables X1,..., Xn are independent and identically distributed with probability…

A: Given information: The probability density function of the random variables X and Y is given.

Q: Suppose that a box contains 9 cameras and that 4 of them are defective. A sample of 2 cameras is…

Q: 4. For a linear combination of n random variables, find its expectation and variance.

Q: Let X be a discrete random variable that takes on the values 2, 3, 4, 5, 6, 7 with respective…

A: X 2 3 4 5 6 7 P(x) 0.15 0.10 0.20 0.20 0.20 0.15

Q: Bob plays a game in which a dice is rolled until an odd number occurs. Bob wins 10 – x dollars if x…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Let X be a random variable that can take values 2, 3, and 5 with probabilities P(X=2)=1/2,…

A: Given P(X=2)=1/2, P(X=3)=1/4, and P(X=5)=1/4.

Q: A psychologist determined that the number of sessions required to obtain the trust of a new patient…

Q: I. TRUE OR FALSE. Write TRUE if the statement is always correct, otherwise write FALSE. TRUE 1. The…

A: 4) A standard normal curve is a normal probability distribution that has a mean of one and standard…

Q: Which of these is not a binomial probability of X~B(12,0.4)? A. P(X-5) = ¹2Co(0.4)5(0.6)7 B.…

A: Let X be the random variable from binomial distribution with probability of success (p) = 0.4 and…

Q: a. Differentiate between a discrete random variables and continuous random variables. b. Forty…

A: Given that a.difference between discrete and continuous random variablesb.given that sample size…

Q: Jensen, arriving at a bus stop, just misses the bus. Suppose that he decides to walk if the (next)…

A: A continuous random variable X is said to follow Uniform distribution with parameters a and b, if…

Q: Suppose X is a random variable with possible values 4,-4 and 2 and with respective probabilities…

A: Its a Discrete probability distribution

Q: Orders come into a pizza place by phone are either for cheese or pepperoni pizza. The time to…

A: Given that the mean time to process and cook a cheese pizza is 3 minutes, Rate parameter, μ=13 Then…

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

Q: Consider a financial asset (for instance a stock) and assume its value today is $100. Let X; be the…

A: To estimate the probability that we make a gain in our investment, It is required to calculate the…

Q: Let X~ binomial (n, p) and Y ~ binomial (m, p) be independent. 1. Derive the MGF of W = X +Y.

A: 3. Given that X~binomial (n, p) and Y~binomial (m, p) The MGF of X is, The MGF of Y is, a)…

Q: Let X be a discrete random variable that takes on the values -2, -1, 0, 1, 2, 3 with respective…

Question

Consider the sample space
{a,b,c,d,e} with probabilities, respectively,
.1,.2,.3,.2,.2. Verify that this is a probability
space. The random variable X is given by
X(a)=1, X(b)=2, X(c)=3. X(d)=4 and X(e)=5.
Compute the expected value and variance of X.
Let X2 be two iterations of X, addeed,
independently. Write down an appropriate
probability space for this and compute the
expected value and variance of X2 two
different ways- directly from the probability
space, and also by using our theorems, (If you
think of X as the outcome of some game, then
X2 is the result of playing the game twice,
independently.)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Multivariate Distributions and Functions of Random Variables$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

A motorcycle drives from Welcome Rotonda to Fairview and back using the same course everyday. There are four stoplights on the course.Let x denote the number of red lights the motorcycle encounters going from Welcome Rotonda to Fairview and y denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (x, y) is given by 2 3 0.07 0.01 0.05 0.01 0.03 0.01 0.03 0.08 0.03 0.02 2 0.03 0.11 0.15 0.01 0.01 3 0.02 0.07 0.1 0.03 0.01 4 0.01 0.06 0.03 0.01 0.01 Find: 1. Standard deviation of Y. 2. Fill in the blanks As the number of motorcycle drivers from Welcome Rotonda to Fairview encountered by the motorcycle (increase, decrease, or be (zero, negative, or positive) covariance. The increases, the number of stoplights of its return trip tends to uncorrelated). Therefore, X and Y have a covariance was calculated to be (numerical value). *Describe the correlation whether a strong, a weak, or no. X and Y have correlation.…
A motorcycle drives from Welcome Rotonda to Fairview and back using the same course everyday. There are four stoplights on the course. Let x denote the number of red lights the motorcycle encounters going from Welcome Rotonda to Fairview and y denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (x, y) is given by 1 2 4 0.01 0.01 0.03 0.07 0.01 0.03 0.05 0.08 0.15 1 0.03 0.02 2 0.03 0.11 0.01 0.01 3 0.02 0.07 0.1 0.03 0.01 4 0.01 0.06 0.03 0.01 0.01 Find: (a) Give the marginal probability distribution of fx (0). (b) Give the marginal probability distribution of fy (3). (c) Give the conditional density distribution of X=3 given Y = 3. (d) Give E(X). . (e) Give E(Y). (1) Give E(X) Y = 3). (g) Give the standard deviation of Y. *Complete the interpretation of the data. As the number of from Welcome Rotonda to Fairview encountered by the motorcycle increases, the number of stoplights of its return trip tends…
I need the answer as soon as possible
Q6
2 A random sample of size 12 drawn from a population of size 200. The sample values and their probabilities are (52,0.004), (72,0.003), (64,0.005), (58,0.003), (42,0.002), (76,0.006), (71,0.006), (63,0.006), (87,0.008), (57,0.002), (61,0.003) and (86,0.007). Estimate population total with a 95% confidence interval by using probability proportional to size sampling.
You are to wait at a bus stop for the bus to arrive. The bus arrives every 30 minutes, but you do not know the exact time (in minutes) it will take to arrive. Thus, you can wait any time (continuous) between 0 and 30 minutes, and you believe all wait times are equally likely. Let X be the random variable of the amount of time in minutes you will wait for the bus. a. What distribution can be used for the random variable X? b. What is the probability that you wait exactly 5 minutes? What is the probability that you wait exactly 5 or 10 minutes? c. What is the probability that you wait more than 20 minutes?
2. A random variable|x has the following probability distribution. Find the value of p and then evaluate the following probabilities: P(X 5) and P(0 < X < 6). Find the mean of the probability distribution. 1 3 4 6 17 P(X) 2p 2p 3p p2 2p2 7p? + p Value of p = P(X < 5) =. P(X 2 5) = P(0 < X < 5) = Mean (u) =
Let X be a discrete random variable with PGF P(s) = a. Find the probability distribution of X. b. Derive the mean and variance of X using its PGF.