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Q: Evaluate: lim (sec z sin z)ot z
A: Note: We are entitles to solve only the first question, unless specified To evaluate :limx→0(sec x…
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Q: What is the Central Limit Theorem? What does an example of it look like?
A: Central limit theorem: Central limit theorem states that, the shape of the sampling distribution of…
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A: The central limit theorem states that if you have a population with mean μ and standard deviation σ…
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A: To integrate: ∫0111+x2dx
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Q: what is the central limit Theorem?
A: Central Limit Theorem:The central limit theorem states that as the sample size increases the sample…
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A: We have to solve
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A: L’Hospital’s Rule : Suppose limx→af(x)g(x) = 00 or limx→af(x)g(x) = ±∞±∞ where a can be any real…
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Q: 15. Let fx)- Find tuntions +3 %3D Flalx) = get (x) =
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A: Determine if the function is continuous or not at a. h(x)=3xx3+x2, a=0
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A: The central limit theorem states that the sampling distribution of the mean approaches a normal…
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Q: Define Contraction Mapping Theorem?
A: The contraction mapping theorem is a method for the construction of solutions of linear and…
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Q: Prove that ) - arctan x + A if x -1 - 4
A: We have to prove: tan-1x-1x+1=tan-1x+3π4 if x<-1tan-1x-π4 if x>-1 Taking LHS, putting…
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Q: tan s lim is Evaluate
A: On directly substituting the limit we obtain indeterminate form 00, so first we need to simplify the…
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Q: 1+cosx Show that if f(x) = In| then f'(x) = -cscx. %3D 1-cosx
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Q: roblem 5: calculate: lim | sin" rdr
A: To calculate: limn→∞∫-11sinnxdx
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A: L' Hospital's rule is used when function makes the form 00 . So you have to take the derivate of the…
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Q: Please poove 18 ŏ bound of (३5) fश्ठ also proove ppes an sup13,5)%35
A: (.) Upper bound: "A number that is greater than or equal to any number in a non-empty subset of ℝ…
Q: Evaluate
A: As per the guidelines we can solve 3 parts only only. Please repost the same for more answers.
Q: when to use the Central Limit Theorem?
A: When repeated samples from the population is drawn and sample statistic for each sample is computed,…
Q: Express the definite integral as a limit of Riemann sums. Do not evaluate! Csc da 3
A: a=3, b=6For each n (number of sub-intervals) , we get∆x=b-an=6-3n∆x=3nAnd for i = 1 , 2 , 3 , . .…
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Q: What are the important concepts about the Central Limit Theorem?
A: The answer is given below.
Q: (2 - de using limit of the Riemann sum.
A: First, find the width and height for the rectangles. Let the number of the intervals be n = 4. The…
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A: Consider the given expression. limx→0sin2x+7x2−2xx2x+12 Simplify the denominator.…
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A: To evaluate this integral , we will use the fundamental theorem of calculus and Lebnitz theorem.
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A: We know that a function gx is continuous at a point p if,limx→pgx=gp.We need to check the continuity…
Q: special fomtion o Show thal (27)
A: We use Gamma function to prove the given result.
Q: what epsilon and delta mean in the epsilon‐delta definition of the limit.
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Q: se the Limit Process to find the aread Ul QUor the given in
A: Given that: The equation is y = 8 - x 3 and the interval [ 1, 3].
Q: @ Hiw/ prove that cosiz=coshz @ Cosh'z @ 1- Tanhz - Sechz
A: As per Bartleby's expert answering policy, we can answer only one question with a maximum of three…
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- An ordinary die is rolled. Find the probability of each event. Rolling a number greater than 4Continuous random variables can assume infinitely many values corresponding to points on a line interval. True FalseConsider a linear birth–death process where the individual birth rate is λ=1, the individual death rate is μ= 3, and there is constant immigration into the population according to a Poisson process with rate α. Please explain and show work! (a) State the rate diagram and the generator. (b) Suppose that there are 10 individuals in the population. What is the probability that the population size increases to 11 before it decreases to 9? (c) Suppose that α = 1 and that the population just became extinct. What is the expected time until it becomes extinct again? α in Greek letter alpha.
- A radioactive mass emits particles according to a Poisson process. The probability that no particles will be emitted in a two-second period is 0.5. What is the probability that no particles are emitted in a four-second period?Distinguish between discrete and continuous random variables. Give an example of each.The Poisson distribution gives the probability for the number of occurrences for a "rare" event. Now, let x be a random variable that represents the waiting time between rare events. Using some mathematics, it can be shown that x has an exponential distribution. Let x > 0 be a random variable and let β > 0 be a constant. Then y = 1 β e−x/β is a curve representing the exponential distribution. Areas under this curve give us exponential probabilities. If a and b are any numbers such that 0 < a < b, then using some extra mathematics, it can be shown that the area under the curve above the interval [a, b] is the following. P(a < x < b) = e−a/β − e−b/β Notice that by definition, x cannot be negative, so, P(x < 0) = 0. The random variable x is called an exponential random variable. Using some more mathematics, it can be shown that the mean and standard deviation of x are the following. μ = β and σ = β Note: The number e = 2.71828 is used throughout…
- We assume that the car accident of a certain driver happen according to a Poisson N(t) of intensity lambda=0.01 per month. Compute the following (a) The probability that the driver has no accident during the first year (b) The probability of exactly one accident during his third year of driving. (c) the probability of at least two accidents before the end of the second year given that there was exactly one accident during the first year.You randomly throw a dart at a circular dartboard with radius R. It is assumed that the dart is infinitely sharp and lands on a completely random point on the dartboard. How do you calculate the probability of the dart hitting the bull's-eye having radius b?A power plant is equipped with 5 emergency generators in case of the mains failing as a result of an earthquake. The failure probability of each generator is attached. a) Assuming all 5 generaors are perfectly correlated (if one fails they all fail), calculate the probability of not being able to provide power via the emergency generator network b) The lifetime of a generator is 20 years. Find the probability of observing no earthquakes during the lifetime of a newly installed generator. Given: rate of earthquakes is 0.25/year on average for any given year probability of observing no earthquakes in any given year = 0.7788
- Accidentally, two depleted batteries get into a set of five batteries. To remove the two depleted batteries, the batteries are tested one by one in random order. Let the random variable X denote the number of batteries that must be tested to find the two depleted batteries. What is the probability mass function of X?A random variable X follows a uniform continuous distribution on the range [0, B]. Use mathematical expectation to show the mean is B/2
