Can someone please explain it to me ASAP??!!! Suppose the reaction temperature X (in °C) in a certain chemical process has a uniform distribution with A = -4 and B = 4.(a) Compute P(X < 0).0.5(b) Compute P(-2 < X < 2).0.5(c) Compute P(-1 s X < 2). (Round your answer to two decimal places.)0.38(d) For k satisfying -4 < k < k + 4 < 4, compute P(k < X < k + 4). (Round your answer to two decimal places.)Need Help?Read ItWatch ItMaster It

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Answered: Suppose the reaction temperature X (in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose the reaction temperature X (in °C) in a certain chemical process has a uniform distribution with A = −6 and B = 6. (d) For k satisfying −6 < k < k + 4 < 6, compute P(k < X < k + 4). (Round your answer to two decimal places.)
In the daily production of a certain kind of rope, the number of defects per foot given by Y is assumed to have a Poisson distribution with mean ? = 4. The profit per foot when the rope is sold is given by X, where X = 70 − 3Y − Y2. Find the expected profit per foot.
At 15:00 it is the end of the school day, and it is assumed that the departure of the students from school can be modelled by a Poisson distribution. On average, 24 students leave the school every minute. (e) There are 200 days in a school year. Given that Y denotes the number of days in the year that at least 700 students leave before 15:30, find (ii) P(Y > 150).
If X(t) is a continuous-time random process with mean value of m and variance of s^2, what is the value of the autocorrelation function at time lag tau=0?
1. Consider the Gaussian distribution N (m, σ2).(a) Show that the pdf integrates to 1.(b) Show that the mean is m and the variance is σ.
Suppose that the time-to-failure of a system has a distribution with the following pdf: f(x) = 0.1e^(-0.1x) What is the probability that the failure occurs between 5 and 20? a). 0.23 b). 0.47 c). 0.088 d). 0
The time for the first widget to be manufactured each morning is random between 1 and 3 seconds with a pdf of f(x)=1/162(x-3)^2(x+6) for 0 < x < 6What is the cumulative distribution function, F(x)? What is the probability of a widget being made earlier than 4 s?Answer to four decimal places What is the probability of a widget being made later than 1.3 s?Answer to four decimal places
Suppose that you enter a fantasy baseball league. Suppose that the 2021 team budget, say , is randomly drawn from a uniform distribution on the interval , where the unit is U.S. million dollars. In addition, suppose that after the value has been observed , the 2022 team budget, say , is randomly drawn from a uniform distribution on the interval . In other words, the 2022 budget is at most as large as the 2021 budget. a) For any given value of x(50<x<350), obtain E[Y|X=x] b) In view of part (a), obtain E[Y|X] c) Atlanta Braves won the 2021 World Series title. Their estimated 2022 payroll is about $130 million. Would your 2022 fantasy baseball budget be on average larger than their 2022 payroll? Explain briefly.
Consider a random variable Y with PDF Pr(Y=k)=pq^(k-1),k=1,2,3,4,5....compute for E(2Y)
Consider a real random variable X with zero mean and variance σ2X . Suppose that wecannot directly observe X, but instead we can observe Yt := X + Wt, t ∈ [0, T ], where T > 0 and{Wt : t ∈ R} is a WSS process with zero mean and correlation function RW , uncorrelated with X.Further suppose that we use the following linear estimator to estimate X based on {Yt : t ∈ [0, T ]}:ˆXT =Z T0h(T − θ)Yθ dθ,i.e., we pass the process {Yt} through a causal LTI filter with impulse response h and sample theoutput at time T . We wish to design h to minimize the mean-squared error of the estimate.a. Use the orthogonality principle to write down a necessary and sufficient condition for theoptimal h. (The condition involves h, T , X, {Yt : t ∈ [0, T ]}, ˆXT , etc.)b. Use part a to derive a condition involving the optimal h that has the following form: for allτ ∈ [0, T ],a =Z T0h(θ)(b + c(τ − θ)) dθ,where a and b are constants and c is some function. (You must find a, b, and c in terms ofthe information…
2) The time between successive customers coming to the market is assumed to have Exponential distribution with parameter l. a) If X1, X2, . . . , Xn are the times, in minutes, between successive customers selected randomly, estimate the parameter of the distribution. b) b) The randomly selected 12 times between successive customers are found as 1.8, 1.2, 0.8, 1.4, 1.2, 0.9, 0.6, 1.2, 1.2, 0.8, 1.5, and 0.6 mins. Estimate the mean time between successive customers, and write down the distribution function. c) In order to estimate the distribution parameter with 0.3 error and 4% risk, find the minimum sample size.
For a non-homogeneous Poisson process, the intensity function is given by λ(t) = 5 if t is in (1, 2] or (3, 4]; λ(t) = 3 if t is in (0, 1] or (2, 3]. Find the probability that the number number of observed occurrences in the time period (1.5; 4] is more than 2. Round answer to 4 decimals.

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