Probability and statistics 1 Random variables 2 Special discrete
... 5.10. In a paper-mill A4 papers are packed in 500-piece packets. The number of sheets in a packet can be considered a normally distributed random variable, whose expected value is 500. (a) What is the standard deviation, if the probability that the number of sheets in a packet is less than 490, is ...
... 5.10. In a paper-mill A4 papers are packed in 500-piece packets. The number of sheets in a packet can be considered a normally distributed random variable, whose expected value is 500. (a) What is the standard deviation, if the probability that the number of sheets in a packet is less than 490, is ...
Summary of the papers on ”Increasing risk” by Rothschild and Stiglitz
... Gn could have been obtained from Fn by a finite number of MPS’s. This theorem results from the two partial results: the first lemma proves it for simple step functions with a finite number of steps and the other one is concerned with approximation of the arbitrary cdf’s F and G to any desired degree by ...
... Gn could have been obtained from Fn by a finite number of MPS’s. This theorem results from the two partial results: the first lemma proves it for simple step functions with a finite number of steps and the other one is concerned with approximation of the arbitrary cdf’s F and G to any desired degree by ...
Rational Expectations and Ambiguity: A Comment on Abel
... propose instead to consider ambiguity averse decision makers defined according to the multiple-priors model of Gilboa and Schmeidler (1989). While our motivation is similar to Chen and Epstein, our approach differs in two important respects. First, while the multiple-priors approach can be used to e ...
... propose instead to consider ambiguity averse decision makers defined according to the multiple-priors model of Gilboa and Schmeidler (1989). While our motivation is similar to Chen and Epstein, our approach differs in two important respects. First, while the multiple-priors approach can be used to e ...
Weighted Sets of Probabilities and Minimax Weighted Expected
... update probabilities, using likelihood (see below). On the other hand, these weights do not act like probabilities if the set of probabilities is infinite. For example, if we had a countable set of hypotheses, we could assign them all weight 1 (so that, intuitively, they are all viewed as equally li ...
... update probabilities, using likelihood (see below). On the other hand, these weights do not act like probabilities if the set of probabilities is infinite. For example, if we had a countable set of hypotheses, we could assign them all weight 1 (so that, intuitively, they are all viewed as equally li ...
Totals, Averages, and Marginals Part 1
... When marginal utility is negative, total utility is getting smaller. You’re adding negative numbers to a positive total. When marginal utility is positive, total utility is getting larger. You’re adding positive numbers to a positive total. ...
... When marginal utility is negative, total utility is getting smaller. You’re adding negative numbers to a positive total. When marginal utility is positive, total utility is getting larger. You’re adding positive numbers to a positive total. ...
HFES2016-1 Foundations of Risk and Risk Management
... Probability tries to look into the future (forecasting), but is hobbled by its reliance on the past Statistics is a tool for trying to make sense of observations (samples) from the past, in an attempt to forecast the future Over the past half millennium, we have made progress; we continue to d ...
... Probability tries to look into the future (forecasting), but is hobbled by its reliance on the past Statistics is a tool for trying to make sense of observations (samples) from the past, in an attempt to forecast the future Over the past half millennium, we have made progress; we continue to d ...
11.4: Bernoulli Trials and Binomial Probability
... Now let’s write all this down in a more precise way: A sequence of experiments is called a sequence of Bernoulli trials, or a binomial experiment, if 1. The same experiment is repeated a fixed number of times. (Each repetition is called a trial.) 2. Only two outcomes are possible on each trial. 3. T ...
... Now let’s write all this down in a more precise way: A sequence of experiments is called a sequence of Bernoulli trials, or a binomial experiment, if 1. The same experiment is repeated a fixed number of times. (Each repetition is called a trial.) 2. Only two outcomes are possible on each trial. 3. T ...
T E C H N I C A L R E P O R T 10024 Prudence, temperance
... respectively by a positive third derivative, by a negative fourth derivative, and by a positive fifth derivative of the utility function. Note that these concepts appear at least indirectly in non-expected utility models (Bleichrodt & Eeckhoudt (2005)). These assumptions are traditionally justified ...
... respectively by a positive third derivative, by a negative fourth derivative, and by a positive fifth derivative of the utility function. Note that these concepts appear at least indirectly in non-expected utility models (Bleichrodt & Eeckhoudt (2005)). These assumptions are traditionally justified ...
Price indices – comparing the arithmetic and geometric mean
... In the case of the arithmetic mean I continue to consume 1 unit of each good (as I alway will regardless of (relative) prices). For the geometric mean, Hicksian (compensated) demand curves with u = 1 are (see below for derivation) x1 (p1 ; p2 ; u) ...
... In the case of the arithmetic mean I continue to consume 1 unit of each good (as I alway will regardless of (relative) prices). For the geometric mean, Hicksian (compensated) demand curves with u = 1 are (see below for derivation) x1 (p1 ; p2 ; u) ...
1 The Psychology of Human Risk Preferences and Vulnerability to
... state in the set is neither 0 nor 1. Choices by DMs under such circumstances can be interpreted as expressing either virtually or literally computed subjective estimates of the relevant probabilities, multiplied by the relative costs and benefits to the DM associated with each possible decision outc ...
... state in the set is neither 0 nor 1. Choices by DMs under such circumstances can be interpreted as expressing either virtually or literally computed subjective estimates of the relevant probabilities, multiplied by the relative costs and benefits to the DM associated with each possible decision outc ...
Special VaRs and the Expected Shortfall
... The historical 1-year loss distribution of a portfolio of loans in € million is well approximated by a N(10,5). What is the 95% VaR? And the 98%? ...
... The historical 1-year loss distribution of a portfolio of loans in € million is well approximated by a N(10,5). What is the 95% VaR? And the 98%? ...
Asteroids: Assessing Catastrophic Risks
... corporate profits. Normal distributions arise when many independent events contribute to some outcome. However when there are unexpected interconnections or catastrophic events, normal distribution can understate 1 the role of small-probability events 2 the role of events that are very far into ...
... corporate profits. Normal distributions arise when many independent events contribute to some outcome. However when there are unexpected interconnections or catastrophic events, normal distribution can understate 1 the role of small-probability events 2 the role of events that are very far into ...
Hot Sticky Random Multipath
... maximize system utility (note: all sources “equal) constraint: bandwidth used less than capacity ...
... maximize system utility (note: all sources “equal) constraint: bandwidth used less than capacity ...
Which Value x Best Represents a Sample x1, ..., xn: Utility
... Need to go beyond the probabilistic case. In many cases, however, we do not have any information about the corresponding probability distribution [6]. How can we then find x e? Utility-based approach. According to the general decision theory, decisions of a rational person are equivalent to maximizin ...
... Need to go beyond the probabilistic case. In many cases, however, we do not have any information about the corresponding probability distribution [6]. How can we then find x e? Utility-based approach. According to the general decision theory, decisions of a rational person are equivalent to maximizin ...
Get - Wiley Online Library
... a probability structure and realistic for application. This latter requirement is key, as unlike a probability distribution the only constraint placed upon a utility function is that it be a bounded function of its arguments. It is therefore quite easy to determine a utility form that satisfies any ...
... a probability structure and realistic for application. This latter requirement is key, as unlike a probability distribution the only constraint placed upon a utility function is that it be a bounded function of its arguments. It is therefore quite easy to determine a utility form that satisfies any ...
Chi‐Square Statistical Analysis of Onion Root Tip Mitosis
... Today, we will be using statistics to test hypotheses, through the Chi‐Square Test. This test compares actual (observed) and predicted (expected) outcomes of an experiment. For each type of outcome (in our case, the phases in mitosis) in the experiment, there are both observed and expected numbers o ...
... Today, we will be using statistics to test hypotheses, through the Chi‐Square Test. This test compares actual (observed) and predicted (expected) outcomes of an experiment. For each type of outcome (in our case, the phases in mitosis) in the experiment, there are both observed and expected numbers o ...
A Minimal Extension of Bayesian Decision Theory
... A (sigma) algebra M of measurable subsets of a state space B—those to which a subjective probability can meaningfully be assigned—is defined to be closed under complements and countable unions. We deviate slightly from the standard definition in allowing M to be empty, noting that M = ∅ implies {∅, B ...
... A (sigma) algebra M of measurable subsets of a state space B—those to which a subjective probability can meaningfully be assigned—is defined to be closed under complements and countable unions. We deviate slightly from the standard definition in allowing M to be empty, noting that M = ∅ implies {∅, B ...
Chi square analysis
... So what does 2.688 mean? Figure out your Degree of freedom (dF) Degrees of freedom can be calculated as the number of categories in the problem minus 1. In our example, there are two categories (green and yellow); therefore, there is 1 degree of freedom. ...
... So what does 2.688 mean? Figure out your Degree of freedom (dF) Degrees of freedom can be calculated as the number of categories in the problem minus 1. In our example, there are two categories (green and yellow); therefore, there is 1 degree of freedom. ...
Academic Year 2013-2014 Course Presentation
... Tangency condition between the budget line and the indifference curves. The slope of the budget line (which is equal to the relative price of the two goods p1/p2) is equal to the slope of the indifference curve (which is equal to the marginal rate of substitution). Budget condition: the optimal bund ...
... Tangency condition between the budget line and the indifference curves. The slope of the budget line (which is equal to the relative price of the two goods p1/p2) is equal to the slope of the indifference curve (which is equal to the marginal rate of substitution). Budget condition: the optimal bund ...
E(X 2 )
... The expected value of a binomial RV based on the number of successes in n identical and independent Bernoulli trials in each of which the probability of Success is p. ...
... The expected value of a binomial RV based on the number of successes in n identical and independent Bernoulli trials in each of which the probability of Success is p. ...
國立高雄大學統計學研究所 碩士論文
... and convex at negative part. The decision weights are the transform of the probabilities of expected utility theory. The idea of transformation is to assign more weight for the outcome that has lower probability and assign less weight for the outcome which has higher probability. So, we can explain ...
... and convex at negative part. The decision weights are the transform of the probabilities of expected utility theory. The idea of transformation is to assign more weight for the outcome that has lower probability and assign less weight for the outcome which has higher probability. So, we can explain ...
Conditional Probability and Expected Value
... Let B be the proposition that it was a blue cab. Let R be the proposition that it was a red cab. Let ”B” be the proposition that the witness said it was a blue cab. And let ”R” be the proposition that the witness said it was a red cab. Given that the witness said it was a blue cab, what’s the probab ...
... Let B be the proposition that it was a blue cab. Let R be the proposition that it was a red cab. Let ”B” be the proposition that the witness said it was a blue cab. And let ”R” be the proposition that the witness said it was a red cab. Given that the witness said it was a blue cab, what’s the probab ...
Homework assignment #1 (20 points)
... a) Find the probability that a given Monday either two or three or four students will be absent (1 point) b) Find the probability that on a given Monday more than three students are absent (1 point) c) Compute the expected value of the random variable X. Interpret this expected value. (1 point) d) C ...
... a) Find the probability that a given Monday either two or three or four students will be absent (1 point) b) Find the probability that on a given Monday more than three students are absent (1 point) c) Compute the expected value of the random variable X. Interpret this expected value. (1 point) d) C ...
Link to Lesson Notes - Mr Santowski`s Math Page
... The net change in your financial holdings is −$1 when you lose, and $35 when you win, so your expected winnings are..... Outcomes are X = -$1 and X = +$35 So E(X) = (-1)(37/38) + 35(1/38) = -0.0526 ...
... The net change in your financial holdings is −$1 when you lose, and $35 when you win, so your expected winnings are..... Outcomes are X = -$1 and X = +$35 So E(X) = (-1)(37/38) + 35(1/38) = -0.0526 ...