Consider a random variable X with support [0, ∞), pdf f, and CDF F. The function h defined as h(x) = f(x)/1 − F(x) for x > 0. The function h is called the failure rate or the hazard function of X. What is the failure rate if X is exponential with parameter λ?

Q: b. What is the critical path? A-C-F-H A-D-G-H OB-E-G-H A-D-F-H c. What is the expected project…

A: Given,The following represents a project that should be scheduled using CPM:ACTIVITYIMMEDIATE…

Q: what is the probability that the sum of the upturned faces will equal 7 when two dices are rolled?

A:

Q: A certain population consists of 5000 individuals.  Of these, 52% are female and 48% are male. The…

A: Population size N =5000Sample size n= 40Percentage of females = 52%Percentage of males = 48%

Q: Consider a non-negative discrete random variable X assuming values from {a1, a2,...}. Prove that…

A: The objective of the question is to prove that the expected value of a non-negative discrete random…

Q: fair coin is flipped three times. What is the probability that there will be at least two heads?…

A: A fair coin is flipped three times.Sample space: S = (HHH, HHT, HTH, THH, TTH, THT, HTT, TTT)

Q: Show that a Hilbert space is closed. Also, for any square-integrable random variable X, show that…

A: The objective of this question is to prove that a Hilbert space is closed and that for any…

Q: Consider a continuous random variable X such that P (−1 ≤ X ≤ 1) = 1/2. Can X be characterized by i)…

A: The objective of the question is to determine whether the given continuous random variable X can be…

Q: A biased coin has a 2/3 probability of landing heads and a 1/3 probability of landing tails. You…

A: The coin is tossed  times.The probability of landing heads: , andThe probability of landing tails:

Q: You are playing a simple card game with another friend, using a standard 52 card deck: four suits…

A: Total number of cards in standard deck = 52Number of cards from each suit = 13

Q: English and American spellings are rigour and rigor respectively. A man staying at a Parisian hotel…

A: Let A=writer is an AmericanE=writer is English manV=a letter found to be a vowelP(A)=0.6P(E)=0.4

Q: For questions with counting, please leave your answers as the sum and/or product of numbers. For any…

A: Please see the explanation section for the solution to the question…

Q: [4] a) Suppose that the transition matrix is P = Is there a stationary distribution for this model.…

A: a)

Q: Recall that a permutation of {1, 2,..., n} is a one-to-one correspondence P from the set {1, 2, ...,…

A: Given that N be an integer whose digits are .

Q: Consider a random sample X₁,..., X, from the density f(x | 0) = -1/0 for x ER (a) Find the MLE Ô for…

A: The probability density function of random variable x is given as:The maximum likelihood estimator…

Q: 0.4 0 0.6/ Find P{X₂= 1, X3 = 1|X₁ = 0}. Hint. P{X2= 1, X3 = 1|X₁ = 0} = P{X3 = 1|X₁ = 0, X₂ =…

A: It is given that the {Xn} be a MC with the state space E = {0, 1, 2} and the TPM is P.

Q: Compute the probability that 10 married couples are seated at random at a round table, then no wife…

A: The number of married couplesThe total number of people seated at the random table (i.e. )

Q: Text In a population of employees in a large company, 15% are certified in a particular skill.…

A: The binomial distribution Given that in a population of employees in a large company, 15% are…

Q: Let P = be a TPM of some homogeneous MC. Investigate if the MC is irreducible and if it is not, give…

A: To investigate whether the given Markov Chain (MC) described by the transition probability matrix…

Q: One coin in a collection of 13 is rigged to have a probability of showing heads equal to 0.6. The…

A: et R shows the event that a rigged coin is selectedand F shows the event that a fair coin is…

Q: Inside a bag there are 3 green balls. 2 red balls and 4 yellow balls. Two balls are randomly drawn…

A:

Q: Three Bananas and three oranges are kept in a box. If two fruits are chosen at random, Find the…

A:

Q: According to a survey released in a press 4985 people were surveyed:- 2975 people said that they…

A:

Q: Discrete random variable Y has the CDF FY(y) as shown below. Find the variance of the random v

A: From the given plot,The pdf of Y is

Q: Q)DETERMINE THE PROBABILITY THAT A NUMBER LESS THAN 4 WILL BE ROLLED WHEN ROLLING A DIE? a)(1/2)…

A:

Q: You roll a 12-sided die. Let A = {8, 9, 11} and B = {4, 7, 8, 11, 12). Find the following. S = {…

A: Given,You roll a 12-sided die.Let A = {8, 9, 11} and B = {4, 7, 8, 11, 12}

Q: In Exercises 1-4, identify the sample space of the probability exp determine the number of outcomes…

A: Since you have posted multiple questions with multiple subparts, we will provide the solution of…

Q: Q9) In University of California among the placement cell, P(students getting placed )=2n/9,…

A: P(students getting placed)=P(students not getting placed)=

Q: An automobile manufacturer is concerned about a fault in the braking mechanism of a particular…

A: a)Suppose a random variable x defines the number of cars per year that will experience the…

Q: In a survey of consumers aged 12 and older, respondents were asked how many cell phones were in use…

A: From the given information ,Total respondents = 201 + 296 + 376 + 138 + 117 .…

Q: A and B are mutually exclusive events. If P(A)=0.07692 and P(B)=0.25, what is the probability P(AUB)…

A:

Q: Let E₁, E2,... → No be a sequence of iid (independent and identically distributed) r.v.'s with the…

A: To show that the sequence {Xn} is a time-homogeneous Markov Chain (MC), we need to demonstrate two…

Q: 2. Find the following probabilities. Provide a graph for each case. a. P(0-0.77) c. P(-0.43<z<1.35)

A: P(0&lt;Z&lt;1.46)

Q: Example: If one die is rolled, find the probability that the first "4" occurs on the eighth roll.…

A: A single die is rolled, and its outcomes are written as follows:

Q: Of 12 possible building sites for factories, 5 have buried toxic waste sites that no one told you…

A: It is given thatThe total number of sites = 12No. of toxic waste sites = 5

Q: An urn contains 3 white and 10 black balls. A fair die is rolled and that number of balls are chosen…

A: An urn contains 3 white and 10 black balls.Let  denote the event of getting i on a dice roll.Let W…

Q: Suppose that a single binary digit (0 or 1) is to be transmitted through a transmission channel.…

A: The objective of this question is to determine the probability of receiving the digit 1, the…

Q: Given the following Venn diagram, find n[(ABC) ООО С 25 23 26 24 A 2 7 C 3 в

A:

Q: A researcher claims that the ages of people who go to once a year are distributed as shown in the…

A: Claim: The ages of people who go to the movies at least once a year are distributed as shown…

Q: A type of system that is employed in engineering work is a group of parallel components or a…

A: Considering that if any one of the components is still functional, the system will not fail since…

Q: lected at random and asked their opinion, what is the probability that at most 7 favor the new tax?…

A: Let X : number of person favor the new tax Against= 4800Total= 16000P = Sample size n = 16x = 7…

Q: Consider a web-server that receives web requests at an average rate ? of 20 requests per second that…

A: Given that,Average rate ? = 20 requests per second, following a Poisson distribution.The answers to…

Q: A survey of hospital patients is taken to determine preference for chicken soup or vegetable…

A: The objective of the question is to fill in the contingency table based on the given data and then…

Q: EXAMPLE 5a If the number of items produced in a factory during a week is a random variable with mean…

A:

Q: An insurance company insured 2000 scooter drivers, 4000 car drivers, and 6000 truck drivers. The…

A: According to the given information,Number of scooter drivers insured, n(Is) = 2000Number of car…

Q: On average, 4 traffic accidents per month occur at a certain intersection. Complete parts (a)…

A: From the information, given thatLet X denotes the number of accidents occur per month at a certain…

Q: For what (natural number) value of j is b(540, 0.8, j) maximized? That is, if 0 ≤ k ≤ 540, then…

A: The objective is to check if  is an integer or not in order to determine the value of that…

Q: A deck consists of playing cards that can have one of 12 suits and one of 6 ranks. A hand is a set…

A: It is required to find the number of possible four of a kind hands from the deck, and the…

Q: consider cdf for random variable X given Fx (x) = x when 0 [a]

A:

Q: For the probability distribution, find d. P(y = 6) e. f(y = 4) f. f(y= 6) g. F(y = 5.5) h. F(4) f.…

A: Since total probability is always 1:P(Y=−2)+P(Y=−1)+P(Y=0)+P(Y=1)+P(Y=2)=1

Q: An urn consists of 3 green balls, 4 blue balls, and 6 red balls. In a random sample of 5 balls, find…

A: The provided information is as follows:The total number of green balls is .The total number of blue…