(a) P(X₁> 1) = P(X2 < 2) (b) Cov(X1, X2) = 0. (c) E(X₁ · X2) = E(X1) · E(X2) (d) P(X₁ > 0) = P(X2 > 0) (e) E ([×1-¹]²) = E ([×2−2]²)
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Let X_1 ∼ N (1, 1) and X_2 ∼ N (2, 4) be two
![(a) P(X₁> 1) = P(X2 < 2)
(b) Cov(X1, X2) = 0.
(c) E(X₁ · X2) = E(X1) · E(X2)
(d) P(X₁ > 0) = P(X2 > 0)
(e) E ([×1-¹]²) = E ([×2−2]²)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6035f1a2-2c03-490a-9469-88f7b64e730f%2F0707359a-ce8d-488e-8fa7-ce168547ffc3%2Fexbeb5k_processed.png&w=3840&q=75)
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- average of 4 people per hour arrive at a shop. Assume the Poisson distribution is a reasonable model for describing the random variable X for the number of arrivals during a given hour. what is the propability of exactly 6 customers arriving during an hour.It is known that 51% of American college students fail a course during their freshman year. A university journal club randomly samples 9 upperclassmen and asks them if they failed a course during their freshman year, 3 say they have. Suppose a hypothesis test is to be conducted to determine if the proportion of students who failed a course during their freshman year is less than 0.51. The random variable is X = the number of students in the sample that failed a course during their freshman year. What values of X are considered "as or more unusual" than the observed count if the null hypothesis is true? X ≥ 3 3 ≤ X ≤ 4.59 X ≥ 4.59 X ≤ 4.59 X ≤ 3The main exit gate has an outflow rate of 20 cars per minute which can be modeled as a Poisson Random Process. Suppose the south gate is also opened and given that cars choose it 34% of the time. What will be the new average time it takes for a car to exit the main gate? (Use 3 sf, in seconds)
- The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.3 minutes and a standard deviation of 3.5 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.) (b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.) (c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)a manufactoring company produces 10,000 platics cups per day. This company supplies cups to a supermakret which sells them in packs of 10 per pack. Ig less than two of a ranfdomlu slected pack (of 10 cups) from the order are defective, the supermarket accepts the whole order. The proportion of defective cups produced by the manufactoring company is 10%. Let X be the random variable representing the number of defective cups in a pack. i) identify the type of distribution being described in this question and write down the value of its parameters. ii) what is the probability that the order will be accepted? iii) What is the probability that a randomly selected pack (of 10 cups) has more than two defective cups?Eye of Jade is a pretty popular tatoo parlor here in Chico, with on averge 1 walk-in customers a day. Assume that people randomly decide to get a tatoo that day and walk in to Eye of Jade independently of other patrons. What is the expected value and variance of of the number of walk-in customers that Eye of Jade can expect to see in a week.
- The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.6 minutes and a standard deviation of 2.9 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 34 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)(b) What is the probability that for 34 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)(c) What is the probability that for 34 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)The executives at a software company called Front Line are trying to decide if they should continue to provide free coffee in their breakrooms. They have 79 employees and each employee has a 67% chance of drinking coffee in the break room each day. Recall, for a binomial random variable, dbinom(j,n,p) P(Y= j) and pbinom(j,n,p) = P(Y < j). What is the standard deviation of employees who will drink coffee in one day?A manufacturer of semiconductor devices takes a random sample of 100 chips and tests them, classifying each chip as defective or non-defective. Let X, 0 if the chip is non-defective and X; = 1 if the chip is defective. The sample fraction defective is X, +X, +---+ X, 100 What is the sampling distribution of the random variable "P?
- Q2: The number of failures of a testing instrument from contamination particles on the product is a Poisson random variable with a mean of 0.02 failures per hour. (a) What is the probability that the instrument does not fail in an 8-hour shift? (b) What is the probability of at least one failure in a 24-hour day?Show that (1) the mean value of a weighted sum of random variables equals the weighted sum of the mean values and (2) the variance of a weighted sum of N random variables equals the weighted sum of all their covariances.In a human genome there are 6.4X109 basepairs and the mutation rate per generation per basepair is 1.8X10-8 basepairs. What is the expected number of new mutations (not carried by either of your parents) present in you? What is the probability that you contain 20 new mutations? Use Poisson distribution to solve.
