Theorem 1.4 (Chebyshev's inequality)(i) Suppose that Var X < ∞. ThenVar XP(X EX>x)≤-x > 0.2(ii) If X1, X2,..., X, are independent with mean 0 and finite variances, thenΣτη Var XeP(|Sn| > x)≤x > 0.(iii) If, in addition, X1, X2, Xn are identically distributed, thennVar XiP(|Sn> x) ≤x > 0.x²

Proof of Chebyshev's Inequality for a Single Random VariableStatement of the TheoremLet X be a…

Answered: Theorem 1.4 (Chebyshev's inequality)…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.2: Polynomial Functions

Problem 96E: What is the purpose of the Intermediate Value Theorem?

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What is the purpose of the Intermediate Value Theorem?
Many people believe that the daily change in price of a company's stock in the stock market is a random variable with mean 0 and variance o² during the middle 2 months between 2 earning report dates when there is not much news released. That is, if Yn represents the closing price of the stock on the nth trading day of that period, then Yn = Yn-1+Xn, for 1 ≤ n ≤ 60, where X₁, X2,..., X60 are independent and identically distributed random variables with mean 0 and variance o². Suppose that the stock price at the beginning of the 2-month period is 100. If o = 2, what is the approximate probability that the stock's closing price on the 30th trading day will exceed 110, i.e., what is P(Y30 > 110)
2 If X₁ and X₂ are the means of independent ran- dom samples of sizes n₁ and n₂ from a normal population with the mean u and the variance o2, show that the vari- ance of the unbiased estimator 2 w X₁ + (1-w). X₂ is a minimum when @ = n1 n₁ + n₂ idnu
Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; is
X = factorial(3) def factorial(n): if n == 1:return 1else:return n* factorial (n-1) def factorial(n):if n== 1: return 1else: 2return n * factorial(n-1) def factorial(n):if n==1: return 1 else:return n* factorial (n-1) Provide a relationship with the domain subset of the integers that is proven using mathematical induction
"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form. x >1 f(x) =10 xs1 (a) Determine the value of k for which f(x) is a legitimate pdf. (b) Obtain the cumulative distribution function. x> 1 F(x) = xs1 (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.)
25. Show that if X is a random variable and g(.) is a Borel measurable function, then Y = g(X) is a random variable.
10. Suppose the probability of selecting a number from the interval [0, 2] is given by f(x) = Cx. (a) Find the value of C so that this is a probability distribution. (b) Find the probability that the given number is in the interval [0,1]. Now find the probability that the selected number is in the interval [1, 2]. The answers differ. Why? (c) If X (x) = x is the random variable giving the value of the selected number, what is E(X)? The Var(X)?
X,X, and X, is a random sample of size 3 from a population 3. with mean value u and variance o2, T, T, T, are the 3. estimators used to estimate mean value u, where T=X,+X,-X,T,= 2X,+3X, - 4X,& T, ax,+x,+x) 1 (ax,+X,+X,) (i) Are T, and T, unbiased estimators ? 1 2 (ii) Find the value of such that T, is unbiased estimator 3 for u. With this value of A is T, a consistent estimator ? (iii) 3 (iv) Which is the best estimator ?
"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period o heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form. x! f(x) = (a) Determine the value of k for which f(x) is a legitimate pdf. (b) Obtain the cumulative distribution function. F(x) = x< 1 (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to three decimal places.) 016 Use the cdf from (b) to determine the probability that headway is between 2 and sec. (Round your answer to three decimal places.) .014 (d) Obtain the mean value of headway and the standard deviation of headway. (Round your answers to three decimal places.) mean .6 standard deviation (e) What is the probability that headway is within 1…
Suppose X~ Binom(6, p) and define an estimator T ==to estimate p. Then, variance 6. of T is, p(1–p) a) Var (T)= 6. b) Var (T) = 6 p(1 – p) c) Var (T)~ p(1-p) d) Var (T) - 36р
if you copy ur answer from other bartleby answers i will dislike

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