Show that if  X is a discrete random variable a mean of  mu and a standard deviation sigma, then  Z=(X-mu)/sigma is a discrete random variable with a mean of zero and a standard deviation of 1

Q: d) Find the probability that at least two particles arrive in a particular 4 second period.

A: An average of 27 particles per minute occurs. The arrival of particles at the counter follows a…

Q: ts, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are arranged in a uniformly random permutation. We denote by a the…

A:

Q: A wheel has 8 equally sized slices numbered from 1 to 8. Some are grey and some are white. The…

A: The total number of slicesThe number of grey slicesThe number of white slices

Q: Of the emails you receive 20% are spam on average. Your spam filter is able to detect 90% of them…

A: P(Spam)=0.20P(not a spam)=1-0.20=0.80P(Detected | Spam)=0.90P(Detected | not a spam)=0.15

Q: Four buses carrying 151 high school students arrive to Montreal. The buses carry, respectively, 35,…

A: There are total 151 students & Bus carry respectively 35,41,31,44 students.

Q: The average time it takes a salesperson to finish a sale on the phone is 9 minutes and is…

A: 2c) According to the given information,Mean, μ = 9 minutes.Let X be a random variable represents the…

Q: construct a spreadsheet simulation to simulate 100 customers and collect statistics on the net order…

A: Given,supermarket customers load their carts with goods totaling between  uniformly (and…

Q: Four buses carrying 148 students from the same school arrive at a football stadium. The buses carry,…

A: Four buses carrying 148 students , Bus1 = 40 studentsBus2 = 33 studentsBus3 = 25 studentsBus4 = 50…

Q: From the following table of joint pdf's, calculate P(T=41A=2).(Answer in percentage terms, but…

A: T=1T=4A=20.21A=50.290.34

Q: Prove that if X and Y are non-negative independent random variables, then X^2 ⊥ Y ^2.

A: To prove that if X and Y are non-negative independent random variables, then X^2 and Y^2 are…

Q: A manufacturer has a machine that if it ran all day today has a proba- bility of 0.2 of breaking…

A: Given that, a manufacturer has a machine that if it ran all day today has a probability of 0.2 of…

Q: X and Y are two discrete random variables, Y P X P -1 1/3 and P(X² = Y²) = 1. Calculate: (1) the…

A: X01P(X)1/32/3Y-101P(Y)1/31/31/3

Q: Yet another time, you find yourself the quality control manager for the Acme Widget Company. You are…

A: We are given two different scenarios and asked whether the claims in each scenario are justified or…

Q: Let X₁, X₂,... be independent random variables, each taking a value of either 1 (with probability p)…

A: Given:Let  be independent random variables, each taking a value of either 1 (with probability p) or…

Q: Use the following information for question 3 and 4. An experiment consists of tossing a pair of dice…

A: An experiment consists of tossing a pair of dice.We have to observe the numbers that are on the…

Q: (a) Find the probability that a randomly selected high school student who took the reading portion…

A: X~N( μ , ?)μ=23.2     , ?=5.5Z-score =( x - μ )/?

Q: 2. The continuous random variables X and Y have known joint probability density function 4x 0≤ y…

A: Given the joint probability density function for the continuous random variables X and Y:

Q: Suzan sees a bag of marbles; she grabs a handful at random. She has seen a bag containing 4 red…

A: 4 red marbles3 green marbles2 white marble1 purple marble

Q: n population the probility that a person likes to drink coffee is 0.62, the probability that a…

A: It is given that for a certain population the probability that a person likes to drink coffee is…

Q: wo random variables, x and y, with values 0, 1, or 2, have the joint probability mass fun n in the…

A: We have a joint probability mass function of two random variable X and Y is given as…

Q: Suppose that a bag of toy marbles contains 20 small marbles and 5 large marbles. What is the…

A: It is given that Small marbles = 20Large marbles = 5Total marbles = 25

Q: Given a function f(y) {cye-2y, 04) Find the distribution function

A:

Q: Hint(s) Check My Work In the EAI sampling problem, the population mean is $71,700 and the population…

A: Given,Population mean, μ = 71700Population standard deviation, σ = 4000Using formula,

Q: Let x determine a random variable, and use your knowledge of probability to prepare a probability…

A: A family has 3 children and the number of girls is recorded.For each birth, there is an equal chance…

Q: In a classroom there are 28 tablets which include 5 that are defective. If seven tablets are chosen…

A: In a classroom there are 28 tablets which includes 5 that are defectiveTotal number of tables…

Q: What is the probability of drawing a spade from a deck of playing cards 6 or fewer times in 12…

A: There are 52 cards in standard deck of cards.4 suits in deck of cards , each suit have 13…

Q: Apple juice contains trace amounts of arsenic, measured in parts per billion (ppb). Over the past…

A: YearConcentration20191.4920223.0520202.5320212.3720193.4920192.6220232.820233.6920203.0420221.622021…

Q: Coronary bypass surgery: A healthcare agency reported that 87% of people who had coronary bypass…

A: The sample of coronary bypass patients, The percentage of people who had coronary bypass surgery is…

Q: On Homework Assignment 1, the general consensus was that I was not in a relationship. Although I…

A: Given the regression output :

Q: Find the expected value of the random variable Y by the probability distribution and by the…

A: Given that an exploratory oil well drilled in a particular region should strike oil with probability…

Q: Q 4.3. A fair die is rolled until a 6 is obtained. Let Y be the total number of rolls and X the…

A: Y is the total number of rolls until a 6 is obtained. This is a geometric distribution. In this…

Q: Consider the following properties of a random experiment: 1. There are a fixed number of trials.…

A: We are asked to match the properties to the respective probability distributions.Properties:1. There…

Q: 1. One hundred persons were asked, "Do you favour regional integration?". Of the 35 that answered…

A: It seems you have submitted 3 different questions, as per the guidelines I can solve the first one.…

Q: 4. In recent years the state of Alaska issued license plates consisting of 7 characters. The first…

A: The lincense plates consisting of 7 characters of which three characters and four numeral digits.

Q: Assume that the random variable X is normally distributed, with mean u = 54 and standard deviation 6…

A: The population mean is 54 and the population standard deviation is 8.

Q: The amount of sugar contained in 1-kg packets is actually normally distributed with a mean of μ =…

A: Given thatthe amount of sugar contained in 1-kg packets is normally distributed with mean of 1.03…

Q: Problem 4: A finite state machine has 3 states, labeled {1, 2, 3}. The input of this state machine…

A: Given that a finite state machine has 3 states, labeled {1, 2, 3}. The input of this state machine…

Q: Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi.…

A: Given information:The value of k is calculated below.

Q: Once an individual has been infected with a certain disease, let X represent the time (days) that…

A: and Note : As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In…

Q: 1. Suppose that X1, X2, · · · , Xn are iid (independent and identically distributed). Let E[Xi ] =…

A: Given that X_n are iid with and ,we can determine the expected value and variance of the sum

Q: The number of tickets issued by a meter reader for parking- meter violations can be modeled by a…

A: It is given that, the number of tickets issued by a meter reader for parking meter violations…

Q: Based on an analysis of sample data, an article proposed the pdf f(x) = 0.55e-0.55(x - 1) when x 2 1…

A: Let X be the time spent at the median line.Given that, the pdf of X is

Q: and P(EF)=0.41. Find the following:

A: P(E)=0.73 ,P(F)=0.57 and P(E ∩ F)=0.41

Q: Consider the following transition probability matrix: [0.6 0.2 0.2 P= 0.3 0.4 0.3 0.0 0.3 0.7 a.…

A: transition probability matrix is given:

Q: According to a university's report, only 35% of all surgical operations at that time required an…

A: Given,The percentage of surgical operations requiring an overnight stay at a hospital is = 35%.So,…

Q: An urn contains n=9 balls with different colors. We draw a ball randomly, record the color then…

A: n=9, m=4

Q: Based on historical data, your manager believes that 25% of the company's orders come from…

A: n=81p=0.25

Q: 2. A random variable X = {0, 1, 2, 3} has probability mass function: 1 1 2 Px(0) = Px(1) = Px(2) =…

A: X~{0,1,2,3}

Q: Use the standard normal table to find the z-score that corresponds to the given percentile. If the…

A: Z has follows standard normal distribution with mean zero and standard deviation one.

Q: Customer A and B are being served by two clerks in the post office. Customer C is waiting and he is…

A: Let's consider the possible scenarios:Customer A is served first and leaves last.Customer B is…