2. Let the following lotteries: L has prizes (0, 2, 4, 6) with equal probabilities. L' has prizes(0.1, 3, 5.9) with equal probabilities.(a) Compute the expected values of the two lotteries and verify they are the same.(b) Compute the variances of the two lotteries and verify that the second lottery has abigger variance.(c) One would be tempted to conclude that L second order stochastically dominatesL', that is, any risk averse decision maker would prefer L over L'. Not true, unfor-tunately. Consider a decision maker with the following Bernoulli utility functionu(x) =2x3 + xif x ≤ 3if x > 3Verify that the decision maker is risk averse and that the decision maker prefers L'over L.

Given that, Two lotteries are: L and L'. L has prizes 0,2,4,6. The prizes have equal probabilities.…

Answered: 2. Let the following lotteries: L has…

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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Show that (1) the mean value of a weighted sum of random variables equals the weighted sum of the mean values and (2) the variance of a weighted sum of N random variables equals the weighted sum of all their covariances.
A die has the numbers 1, 2, 2, 3, 3, 3 on its six sides. If the dies is rolled, what is the expected valueand variance of the number showing
b. The brake switch of the 1998 model of Mercedes Benz ML320 needs a replacement. There are similar brake switches with similar shapes but for different brands of vehicles which are all without labels. Past experience has revealed that three (3) different trials or attempts have to be made in order to get the right component fixed. If the random variable X of interest is the number of successful attempts in each combination of the three (3) different outcomes, you are required to 2 | Page 2/3 i. Determine the type of random variable X denotes ii. Obtain the probability distribution for the random variable X iii. Determine the distribution function for X
If P (A) — 0.7, Р(B) — 0.3 and P (АВ) %3 0.2, || (a) Represent these data on a Venn diagram. A В S (i) (ii) (iii) (b) Determine the following probabilities (i) (ii) (iii) (iv) Р (AUB) P (A’ OB) P (A’ U B) P (B| A’)
A system consists of four parts that work independently of each other. Working probabilities of these parts are given as 0.9 , 0.8 , 0.7 and 0.6, respectively. If the random variable X is defined as the total number of parts working in this system, calculate the probabilities P {X>0}, P {X=2} , the expected value and the variance.
A factory produces pen-drives of which 35% are working perfectly. Suppose 20 pen- drives are tested in each box. 4. (a) Use Binomial distribution to find the probability that at most 2 pen-drives in the box are working perfectly. (b) Recalculate the probabilities in part (a) by using Normal approximation.
An experiment can result in one of five equally likely simple events, E₁, E₂, A: E₂, E4 2' P(A) = = 0.4 B: E₁, E3, E4, E5 P(B) = 0.8 C: E₂, E3 Refer to the following probabilities. P(A n B) = 0.2 P(AIB) = 0.25 P(BIA) P(BU C) = 1 P(BIC) 0.5 P(CIB) 0.25 Use the Addition and Multiplication Rules to find the following probabilities. (a) P(AUB) (b) P(An B) = 0.5 P(A U B) = ---Select--- + ---Select--- ✓ P(A n B) = ---Select--- (c) P(B n C) Yes P(B n C) = ---Select--- No P(C) = 0.4 . P(B) = = P(C) = = ---Select--- V = Do the results agree with those obtained by listing the simple events in each? P(A U B) = P({E₁, E₂, E3, E4, E5}) = 1 P(A n B) = P({E₁}) = 0.2 P(B n C) = P({E3}) = 0.2 .., E5. Events A, B, and C are defined as follows.
Let E and F be two events of an experiment with sample space S. Suppose P(E) = 0.46, P(F^) = 0.65, and P(E U F) =0.7. Calculate the probabilities below. (a) P(E) = (b) P(F) (c) P(E n F) =
An arcade machine costs one dollar to play. Every time you play, there is a 1/10 chance of winning.(a) Let A be the number of times you play until you win. Find the variance Var[A].(b) Ten people play the arcade machine; each one keeps playing until they win, and thenit’s the next person’s turn. Let B be the number of times they play in total. Find thevariance Var[B].(c) Ten years later, you come back to the arcade machine, and it’s exactly the same, exceptthat due to inflation, the machine costs $10 to play.Let C be the the total cost of playing until you win. Find the variance Var[C].
One common disease among pediatric patients is streptococcal pharyngitis (strep throat). If a pediatric patient comes in to the pediatricians feeling ill, there is a 26% chance that they have strep throat. A doctor sees 7 pediatric patients on a particular day (assume these patients are independent). Consider the random variable is a binomial random variable such that X = number of pediatric patients with strep throat. What is the expected number of pediatric patients with strep throat?
2 A random sample of size 12 drawn from a population of size 200. The sample values and their probabilities are (52,0.004), (72,0.003), (64,0.005), (58,0.003), (42,0.002), (76,0.006), (71,0.006), (63,0.006), (87,0.008), (57,0.002), (61,0.003) and (86,0.007). Estimate population total with a 95% confidence interval by using probability proportional to size sampling.
4. Let X and Y denote the lengths of life, in years of two components in an electronic system. If the joint density function of these variables is f(x, y) = fe-(x+y),x > 0,y >0 0, elsewhere. Find P(0 < X < 1|Y = 2)

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