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). (b) Compute P(-2 < X < 2). (c) Compute P(-1 ≤ x ≤ 2). (Round your answer to two decimal places.) (d) For k satisfying -4
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Please solve a, b, c, and d.
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thanks for the help but could you solve for d as well as I asked?
- 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.)Suppose the reaction temperature X (in °C) in a certain chemical process has a uniform distribution with A = −6 and B = 6. (a) Compute P(X < 0) (b) Compute P(−3 < X < 3). (c) Compute P(−4≤ X ≤ 5). (Round your answer to two 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.
- IF F(x, y) is the value of the joint distribution function of X and Y at (x, y), show that the marginal distribution function of X is given by G(x) = F(x, ∞) for - ∞ <x < ∞ Use this result to find the marginal distribution function of X for the random variable F(x, y) = { (1-e-x2 ) (1- e-y2) for x>0, y> 0 and 0 elsewhereA 99 percent one-sample z-interval for a proportion will be created from the point estimate obtained from each of two random samples selected from the same population: sample R and sample S. Let R represent a random sample of size 1,000, and let S represent a random sample of size 4,000. If the point estimate obtained from R is equal to the point estimate obtained from S, which of the following must be true about the respective margins of error constructed from those samples? (A) The margin of error for S will be 4 times the margin of error for R. (B) The margin of error for S will be 2 times the margin of error for R. (C) The margin of error for S will be equal to the margin of error for R. (D) The margin of error for R will be 4 times the margin of error for S. (E) The margin of error for R will be 2 times the margin of error for S.1.- A study conducted in the automotive field states that more than 40% of vehicle engine failures are due to problems in the cooling system. To test this statement, a study is carried out on 70 vehicles and the critical region is defined as x < 26, where x is the number of vehicle engines that have problems in the cooling system. (use the normal approximation)a) Evaluate the probability of making a type I error, assuming that p = 0.4.b) Evaluate the probability of committing a type II error, for the alternative p = 0.3.
- If F(x1, x2, x3) is the value of the joint distribution function of X1, X2, and X3 at (x1, x2, x3), show that the joint marginal distribution function of X1 and X3 is given by M(x1, x3) = F(x1, q, x3) for −q < x1 < q, −q < x3 < q and that the marginal distribution function of X1 is given by G(x1) = F(x1, q, q) for −q < x1 < q With reference to Example 19, use these results to find (a) the joint marginal distribution function of X1 and X3; (b) the marginal distribution function of X1.Suppose that the weight of an newborn fawn is Uniformly distributed between 2.5 and 3.7 kg. Suppose that a newborn fawn is randomly selected. Round answers to 4 decimal places when possible. f. P(x > 3 | x < 3.5) =Suppose that the random variables X1,...,Xn form a random sample of size n from the uniform distribution on the interval [0, 1]. Let Y1 = min{X1,. . .,Xn}, and let Yn = max{X1,...,Xn}. Find E(Y1) and E(Yn).
- Let X1,X2,... be a sequence of identically distributed random variables with E|X1|<∞ and let Yn = n−1max1≤i≤n|Xi|. Show that limnE(Yn) = 0Let X1, .... Xn be a random sample from a population with location pdf f(x-Q). Show that the order statistics, T(X1, ...., Xn) = (X(1), ... X(n)) are a sufficient statistics for Q and no further reduction is possible?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.