Answered: For the following discrete variable…

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Probability

For the following discrete variable with probability f(x) X 1 3 4 f(x) 0.2 0.15 20 0.05 0.15 P(1.1

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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For a particular disease, the probability that a patient passes away within the xth year is given by the following table: xx P(x)P(x) 0 0.016 1 0.031 2 0.256 3 0.298 4 0.35 5 0.028 6 0.021 This means that the probability that someone passes away within the first year is 0.016. The probability that they pass away after one year would be 0.031. What is the mean number of years someone survives? (round to two decimal places) What is the standard deviation for the number of years someone survives? (round to two decimal places) The Range Rule of Thumb for survival would be: years to years. (Round each to two decimal places.) In your own words, interpret what the Range Rule of Thumb tells us about this disease. (If you don't remember what the Range Rule of Thumb is, review the heading "Unusual Values" in the Learning Activities.)
An interpolation function, P(x), for e 2 x between x=0 and x=.5 was found using the following data points (0, 1), (0.1, 1.2214), (0.2, 1.4918), (0.3, 1.8221), (0.4, 2.2255), and (0.5, 2.7183). What is the upper bound of the approximation at P(0.25)? a) ( 0.25 ) ( 0.25 – 0.1) ( 0.25 – 0.2 ) ( 0.25 – 0.3 )( 0.25 – 0.4 ) (0.25 – 0.5 ) 6 ! 2 6 e 0.5 b) ( 0.25 ) ( 0.25 - 0.1) (0.25 – 0.2 ) ( 0.25 - 0.3 ) ( 0.25 – 0.4 ) ( 0.25 – 0.5 ) 5!25 e 0.5 c) ( 0.25 ) ( 0.25 – 0.1) ( 0.25 – 0.2 ) ( 0.25 – 0.3 ) (0.25 – 0.4 ) ( 0.25 – 0.5 ) 6 ! 2 6 e d) ( 0.25 ) ( 0.25 – 0.1) ( 0.25 – 0.2) ( 0.25 – 0.3 ) ( 0.25 – 0.4)( 0.25 – 0.5 ) 5 ! 25 e - - (0.25)(0.25-0.1)(0.25-0.2)(0.25-0.3)(0.25–0.4)(0.25–0.5) ,6 ,0.5 6! (0.25)(0.25–0.1)(0.25–0.2)(0.25–0.3)(0.25,0.4)(0.25–0.5) 25 0.5 5! O (0.25)(0.25–0.1)(0.25–0.2)(0.25-0.3)(0.25-0.4)(0.25–0.5) -26e 6! (0.25)(0.25–0.1)(0.25–0.2)(0.25–0.3)(0.25–0.4)(0.25–0.5) ,5. 5!
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Consider the following function for a value of k.f(x) ={3kx/7, 0 ≤ x ≤ 1 3k(5 − x)/7 , 1 ≤ x ≤ 30, otherwise.Comment on the output of these probabilities below, what will be theconclusion of your output.(i)Evaluate k.(ii)find (a) p(1 ≤ x ≤ 2) (b) p(x > 2). (u) p(x ≤ 8/3).
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2. For the following discrete variable with probability f(x) X 1 3 4 5 f(x) 0.2 0.15 2c 0.05 0.15 (a) Determine the value of c Select one: О а. 0.15 O b. 0.225 0.25 O c. none O d. 0.4
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The Arrow-Pratt measures of absolute and relative risk aversion respectively describe the willingness of a consumers to risk a fixed amount of wealth or a fixed fraction of their wealth. This problem will demonstrate this by setting up a simple investment problem. Suppose that consumers begin with initial wealth Wo and may buy shares of a risky asset whose payoff per share is given by 2. (1 w/ prob. P, X = 1-1 w/ prob.1– p. Therefore buying { shares of the risky asset yields final wealth W = Wo +X. Suppose that each consumer may buy an unlimited number of shares, and seeks to maximize expected utility of final wealth max E[u(W)]. (a) Expand the consumer's expected utility maximization problem, and find the first order condition. (b) Let Cara be a consumer whose utility function exhibits constant absolute risk aver- sion UA(W) = 1– e-aW Find Cara's optimal number of shares and show that it does not depend on her starting wealth Wo-