Suppose that you choose three coins at random (without replacement) from a bag containing four 20p coins and five 10p coins. (i) Find the probability mass function of the random variable counting the number of 20p coins selected. (ii) Determine the total expected cash value of the three coins you get, giving your answer correct to the nearest penny. (b) Let ZZ be a discrete random variable with E(Z)=0E(Z)=0. Does it necessarily follow that E(Z3)=0E(Z3)=0? If yes, give a proof; if no, give a counterexample.

Suppose that you choose three coins at random (without replacement) from a bag containing four 20p coins and five 10p coins. (i) Find the probability mass function of the random variable counting the number of 20p coins selected. (ii) Determine the total expected cash value of the three coins you get, giving your answer correct to the nearest penny. (b) Let ZZ be a discrete random variable with E(Z)=0E(Z)=0. Does it necessarily follow that E(Z3)=0E(Z3)=0? If yes, give a proof; if no, give a counterexample.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

See similar textbooks

Related questions

Q: What are the odds against rolling a 4 on a single die?

A: From the provided information, A single die is rolled. Total outcomes = 6 Sample space is as follow:…

Q: A single die is rolled twice. The 36 equally-likely outcomes are shown to the right. Find the…

A: Given:

Q: Construct a 90% Confidence Interval based on the following data: 45, 55, 67, 45, 68, 79, 98, 87, 84,…

A: Method Sample mean and sample sd calculated.

Q: Suppose that Z is a discrete random variable with positive expectation. If Var(Z) = 3 and E(Z²) = 4,…

A: Given that, Z is a discrete random variable with, Var(Z)=3, E(Z2)=4 We have to find E(1 - 4Z), E(Z2…

Q: ould you solve e, please

A: Variables are of two types, they are continuous and discrete variables. Continuous variable has…

Q: 3. (a) How many permutations of the letters ABCDEFGH does there exist? (b) How many permutations of…

A: Given Letters= 8

Q: The trifecta at most racetracks consists of selecting the first-, second-, and third-place…

A: The total number of entries in the trifecta race is, n = 11 There are three finishers are selected…

Q: 6. Buses arrive at ten minute intervals starting at noon. A man arrives at the bus stop a random…

Q: A random variable X is normally distributed with mean 32 and standard deviation 8.2 Find the z…

A: Answer: From the given data, X is a normally distributed random variable Mean μ = 32 Standard…

Q: : Let (X, r≥ 1} be the integer-valued identically distributed intervals between the times of a…

Q: A traditional fair die is thrown twice. What is the probability that: a) a six turns up exactly…

A: Here total number of out comes are 62=36 Sample space…

Q: A hat contains four marbles: 1 yellow, 1 red, 1 blue, and 1 green. Two marbles are to be randomly…

A: As per our guidelines I can solve only first three subparts. Kindly post the remaining subparts…

Q: quiz consists of 24 multiple choice questions. Each question has 5 possible answers, only one of…

A: given data, 24 multiple choice question each question has 5 possible answers,only one of which is…

Q: We toss n coins, and each one shows heads with probability p, independently of each of the others.…

Q: Express the confidence interval 59.3 % 8.3% in interval form. Express the answer in decimal format…

A: The given confidence interval is 59.3%±8.3%.

Q: Customers arrive at a local store at a rate of 10 per hour. a. What is the probability that, in any…

A: Given that: Customers arrive at a local store at a rate of 10 per hour.

Q: Suppose that X and Y are random variables with joint density function = fx,x (x,y) = 8xy for 0<y< x…

Q: Find area to the left of z= -1.3

A: We will use Excel to find the required area under standard Normal curve.

Q: Find the median for the given data 16, 4, 7, 9 , 11, 27, 32, 44, 88

A: Answer: Given data is, 16, 4, 7, 9 , 11, 27, 32, 44, 88 Number of values = n = 9

Q: A pair of dice are tossed. What is the probability of getting a total of 8 by getting the sample…

A: A pair of dice are tossed.

Q: A science class has 3 girls and 9 boys in seventh grade and 5 girls and 3 boys in eighth grade. The…

A: Given In seventh grade=3 girls,9 boys In eighth grade=5 girls,3 boys

Q: A data-collection method that consistently either under-or-overestimates a characteristic of the…

A: The objective is to identify the bias caused by a data collection method that consistently either…

Q: If Z1, Z2, Z3 are independent and identically distributed, such that Zi--Geom(0.4) for i=1,2,3. What…

Q: Consider the pmf: f(x) = P(X = x) x, if x = {1, 2, 3} € 0, otherwise. Show that P(X = x) is indeed a…

A: Answer: - Given, the probability mass function f(x) = P(X = x) = 16xif x ∈{1, 2,…

Q: Since the length of a downhill ski is related to the height of the individuals renting them, it is…

A: Given,Mean(μ)=150standard deviation(σ)=10

Q: Buffon's needle revisited. Two grids of parallel lines are superimposed: the first grid contains…

Q: Consider the pmf. f(x) = P(X = x) = = {x, if x € {1,2,3} 0, otherwise. Show that P(X = x) is indeed…

A: Given pmf is; f(x) = P(X=x) = 16x,x∈{1,2,3}0otherwise

Q: Consider the following data x,-7,-6,-5,-4,-3 P(X=x) 0.2,0.2,0.2,0.2,0.2 find the value of P(X < -4)…

A: Given X -7 -6 -5 -4 -3 P(X=x) 0.2 0.2 0.2 0.2 0.2

Q: K 6: Statistical Inference a. You have the following data of wind speed (in mph) in Ithaca, NY at 3…

A: Given data:: x=c(10,7,3,9,7,9,12,13,1,12) By using R-software…

Q: Prove that P(A | B) = P(B | A)P(A)/P(B) whenever P(A)P(B) 0. Show that, if P(A | B) > P(A), then P(B…

Q: Find the critical value x corresponding to a sample size of 107 and a confidence level of 99%.…

A: Followings are the Explanation of the question ANSWER :- Confidence interval for population…

Q: 1. We are rolling 2 fair dice each with n sides. We will roll both and the the largest outcome of…

Q: 7) A decision maker who is considered to be a risk taker is faced with this set of probabilities…

A: Given that, The decision maker who is considered to be a risk taker is faced with this set…

Q: The patient recovery time from a particular surgical procedure is normally distributed with a mean…

A: Since you have posted multiple questions, we are allowed to slove only first three, please repost…

Q: 3. The following equations are incorrect since the r.h.s. is unfinished. Please add whatever is…

A: The equations of the RHS are incorrect for the given question. The objective is to set the correct…

Q: Let X be a Markov chain and let (nrr≥ 0} be an unbounded increasing sequence of positive integers.…

Q: A financial services committee had 60 members, of which 11 were women. If 10 members are selected at…

A: Given;total number of members in a financial services committee = 6060 members = 11 women + 49 menif…

Q: The length of time required by students to complete a one-hour exam is a random variable, X, with…

Q: The following table shows U.S. employment figures for 2014, broken down by educational attainment.…

A: The education attainment is distribution by the above table.

Q: A coin is tossed repeatedly, and heads turns up with probability p on each toss. Let hn be the…

Q: Suppose that X and Y have the joint probability mass function x+y 21 P (X = x, Y = y) = " X = 1, 2,…

A: Given information: The joint probability mass function is, PX=x,Y=y=x+y21, x=1,2,3 and y=1,2 Let…

Q: (b) Let Z be a discrete random variable with E(Z) = 0. Does it necessarily follow that E(Z³) = 0? If…

A: Given that, Z is discrete random variable. We know that, E(z)= ∑Zi*p(zi) Where p(zi) is the…

Q: Is the probability for my standardized range really the same as for my original distribution? How…

A: introduction the above question is about probability We have to explain is the probability for…

Q: Inference of the population mean with small samples Show development for the solution In an…

A: Given that, in an clinic, a certain group of people is on a program to lose weight and improve their…

Q: If n-470 and p (p-hat) -0.25, find the margin of error at a 99% confidence level Give your answer to…

Q: Consider the pmf: f(x) = P(X = x) = 6* = { ² x, if x = {1, 2, 3} 0, otherwise. Show that P(X = x) is…

Q: 5. How many words from the Roman alphabet (26 letters) of length 45 have (a) No A's? (b) At least…

Q: A company manufacturing computer chips finds that 8% of all chips manufactured are defective.…

A: Note: As per the Bartelby guidelines only three subparts can be answered. Kindly, resubmit for…

Q: 9. Represent the following relations on A = {1, 2, 3, 4, 5, 6} using a matrix and a digraph. (a) R =…

A: Given that , A = { 1,2,3,4,5,6}

Q: An aluminum foil manufacturer wants to improve the quality of his product and is trying to develop a…

Question

a) Suppose that you choose three coins at random (without replacement) from a bag containing four 20p coins and five 10p coins.

(i) Find the probability mass function of the random variable counting the number of 20p coins selected.

(ii) Determine the total expected cash value of the three coins you get, giving your answer correct to the nearest penny.

(b) Let ZZ be a discrete random variable with E(Z)=0E(Z)=0. Does it necessarily follow that E(Z3)=0E(Z3)=0? If yes, give a proof; if no, give a counterexample.

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

Expert Solution