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(a)
To find: Whether the given variable is discrete or continuous.
(a)
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Answer to Problem 8.1E
The given variable is discrete.
Explanation of Solution
Given:
The variable is “Number of commercials that are shown”.
A variable whose value is determined by counting is referred to as a discrete variable. A continuous variable is one whose value may be determined through measurement.
In this case, the given variable, the number of commercials shown, can be counted and does not take unrounded values. Thus, it can be considered an example of a discrete random variable.
Therefore, the variable is a discrete variable.
(b)
To find: The given variable is discrete or continuous.
(b)
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Answer to Problem 8.1E
The given variable is continuous.
Explanation of Solution
The given variable is the length which is noted in seconds. The variable's length can take any value within a certain
Therefore, the variable is continuous.
(c)
To find: The given variable is discrete or continuous.
(c)
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Answer to Problem 8.1E
The given variable is discrete.
Explanation of Solution
In this case, the given variable is the number of accidents recorded. The variable can only have two values that can be counted and do not take unrounded values. Thus, it can be considered an example of a discrete random variable.
Therefore, the variable is discrete.
(d)
To find: The given variable is discrete or continuous.
(d)
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Answer to Problem 8.1E
The given variable is discrete.
Explanation of Solution
In this case, the given variable is whether the rain is predicted. The variable can only have two values that can be counted and do not take unrounded values. Thus, it can be considered an example of a discrete random variable.
Therefore, the variable is discrete.
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Chapter 8 Solutions
Mind on Statistics
- Theorem 1.2 (1) Suppose that P(|X|≤b) = 1 for some b > 0, that EX = 0, and set Var X = 0². Then, for 0 0, P(X > x) ≤e-x+1²² P(|X|>x) ≤2e-1x+1²² (ii) Let X1, X2...., Xn be independent random variables with mean 0, suppose that P(X ≤b) = 1 for all k, and set oσ = Var X. Then, for x > 0. and 0x) ≤2 exp Σ k=1 (iii) If, in addition, X1, X2, X, are identically distributed, then P(S|x) ≤2 expl-tx+nt²o).arrow_forwardTheorem 5.1 (Jensen's inequality) state without proof the Jensen's Ineg. Let X be a random variable, g a convex function, and suppose that X and g(X) are integrable. Then g(EX) < Eg(X).arrow_forwardCan social media mistakes hurt your chances of finding a job? According to a survey of 1,000 hiring managers across many different industries, 76% claim that they use social media sites to research prospective candidates for any job. Calculate the probabilities of the following events. (Round your answers to three decimal places.) answer parts a-c. a) Out of 30 job listings, at least 19 will conduct social media screening. b) Out of 30 job listings, fewer than 17 will conduct social media screening. c) Out of 30 job listings, exactly between 19 and 22 (including 19 and 22) will conduct social media screening. show all steps for probabilities please. answer parts a-c.arrow_forward
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- Theorem 7.2 Suppose that E X = 0 for all k, that Var X = 0} x) ≤ 2P(S>x 1≤k≤n S√2), -S√2). P(max Sk>x) ≤ 2P(|S|>x- 1arrow_forwardThree players (one divider and two choosers) are going to divide a cake fairly using the lone divider method. The divider cuts the cake into three slices (s1, s2, and s3).If the chooser's declarations are Chooser 1: {s3} and Chooser 2: {s3}, which of the following is a fair division of the cake?arrow_forwardTheorem 1.4 (Chebyshev's inequality) (i) Suppose that Var X x)≤- x > 0. 2 (ii) If X1, X2,..., X, are independent with mean 0 and finite variances, then Στη Var Xe P(|Sn| > x)≤ x > 0. (iii) If, in addition, X1, X2, Xn are identically distributed, then nVar Xi P(|Sn> x) ≤ x > 0. x²arrow_forwardTheorem 2.5 (The Lyapounov inequality) For 0arrow_forwardTheorem 1.6 (The Kolmogorov inequality) Let X1, X2, Xn be independent random variables with mean 0 and suppose that Var Xk 0, P(max Sk>x) ≤ Isk≤n Σ-Var X In particular, if X1, X2,..., X, are identically distributed, then P(max Sx) ≤ Isk≤n nVar X₁ x2arrow_forwardTheorem 3.1 (The Cauchy-Schwarz inequality) Suppose that X and Y have finite variances. Then |EXYarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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