The annual premium for a $20,000 insurance policy against the theft of a painting is $300. If the (empirical) probability that the painting will be stolen during the year is 0.02, what is your expected return from the insurancecompany if you take out this insurance?CLet X be the random variable for the amount of money received from the insurance company in the given year.E(X)= dollars

Let us assume x is the random variable for the amount received from the Insurance company.

Answered: The annual premium for a $20,000…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose that the random variable xx, shown below, represents the number of speeding tickets a person received in a three-year period. P(x)P(x) represents the probability of a randomly selected person having received that number of speeding tickets during that period. Use the probability distribution table shown below to answer the following questions. xx P(x)P(x) 0 0.3891 1 0.281 2 0.1497 3 0.098 4 0.0471 5 0.0351 6+ 0.0000 What is the probability that a randomly selected person has received four or more tickets in a three-year period?P(x≥4)=What is the probability that a randomly selected person has received more than four tickets in a three-year period?P(x>4)=Help me, please?
Dispatches to the Miami Coast Guard Search & Rescue Division concern either routine or emergency cases. The time to process a routine case is an exponential random variable with an expected value of 3 minutes, while the time to process an emergency case is an exponential random variable with an expected value of 10 minutes. A dispatch is routine with a probability of 0.8, or an emergency with a probability of 0.2. The status of dispatches and processing times are independent across dispatches. Let X be the processing time of the next dispatch. a) Calculate P{X > 4}.b) Calculate E[X].c) Calculate Var(X). (Hint: Var(X) = E[Var(X |Y )] + Var(E[X |Y ]).
In the 2010 U.S. Census, one of the questions asked was “How many people live in your household?” The table below shows the probability distribution of this variable, X. X (Number of People) 1 2 3 4 5 6 7 P(X = x) 0.267 0.336 0.158 0.137 0.063 0.024 0.015 What is the probability that a randomly chosen household has no more than 4 people living in it? 0.898 0.102 0.761 1.961 0.239
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.)
As you walk into your econometrics exam, a friend bets you $10 that she will outscore you on the exam. Let ✗ be a random variable denoting your winnings. X can take the values 10, if you win teh bet, 0 if there is a score tie, or -10 if you lose. You know that the probability distribution for ✗ is denoted by f(x) and it depends on whether she studied for the exam or not. Let Y be the random variable that indicates if she studied, Y = 0 if she studied and Y = 1 if she did not study. The following table denotes the joint distribution of X and Y : Y=0 Y=1 f(x) X = -10 0.18 P1 P2 X = 0 0 P3 0.3 X = 10 P4 0.45 P5 f(y) P6 0.75 Probabilities P1, P2, P3, P4, P5, P6 are not displayed in the table. Answer the following items: (a) (b) (a) Compute the Probabilities P1, P2, P3, P4, P5, P6 of the table. (b) Compute the expectation E(X). Should you take the bet? (c) What is the probability distribution of your winnings if you know that she did not study, namely, P(X = −10|Y = 1), P(X = 0|Y = 1), P(X…
Suppose that the random variable xx, shown below, represents the number of speeding tickets a person received in a three-year period. P(x)P(x) represents the probability of a randomly selected person having received that number of speeding tickets during that period. Use the probability distribution table shown below to answer the following questions. xx P(x)P(x) 0 0.3891 1 0.281 2 0.1497 3 0.098 4 0.0471 5 0.0351 6+ 0.0000 Would it be unusual to randomly select a person who has received four or more tickets in a three-year period? A. Yes B. NoIs it correct answer B?
Verify whether the given table represents a probability distribution. In those cases where a probability distribution is described, find the mean and standard deviation. NOTE: The Rounding Rule for the mean and standard deviation: They should be rounded to one more decimal place than occurs in the raw data. For a group of four students, the number y who takes the Calculus II class next semester is given by this table. y P(y) 0 0.5131 1 0.3139 2 0.0624 3 0.1102 4 0.2002 Probability distribution with μ=0.4 and σ=0.4 Probability distribution with μ=0.6 and σ=0.1 Probability distribution with μ=0.6 and σ=0.3 Probability distribution with μ=0.7 and σ=0.4
The annual premium for a $15,000 insurance policy against the theft of a painting is $200. If the (empirical) probability that the painting will be stolen during the year is 0.01, what is your expected return from the insurance company if you take out this insurance? ..... Let X be the random variable for the amount of money received from the insurance company in the given year. E(X) = dollars %3D
Luz has noticed the probability distribution for X = number of cars in line to use the drive-thru ATM when she visits her bank is shown below. X 0 1 2 3 4 P(X) 0.10 0.10 0.40 0.30 0.10 What is the probability mean number of cars in line for the drive-thru ATM when Luz visits her bank?
The joint probability distribution of the number X of cars and the number Y of buses per signal cycle at a proposed left-turn lane is displayed in the accompanying joint probability table below. y P(xy) 1 2. 0. .025 .015 .010 .050 .030 020 2. .125 .075 050 3. 150 090 060 4. 100 .060 040 050 .030 .020 Suppose the left-turn lane is to have a capacity of six cars, and that one bus is equivalent to three cars. What is the probability of an overflow duringa cycle? Select one: O 48 O 28 O38 0.18
In an uncertain economy, Americans tend to keep spending down. Let x be the amount of money U.S. individuals spend on groceries monthly. Suppose the probability distribution of x is a uniform distribution from $300 to $400 which is represented by the picture below. f(x) 0.010 0.008 0.006 0.004 0.002 300 320 340 360 380 400 X i (a) What is the probability that a randomly selected individual spends between $315 and $370 on groceries each month? (b) Determine whether the following statement is true or false. The variable, the amount an individual plans to spend on groceries per month, is a numerical (quantitative) variable. True O False
Jim is a 60-year-old Anglo male in reasonably good health. He wants to take out a $50,000 term (that is, straight death benefit) life insurance policy until he is 65. The policy will expire on his 65th birthday. The probability of death in a given year is provided by the Vital Statistics Section of the Statistical Abstract of the United States (116th Edition). x = age 60 61 62 63 64 P(death at this age) 0.01156 0.01348 0.01615 0.01999 0.02266 Jim is applying to Big Rock Insurance Company for his term insurance policy. (a) What is the probability that Jim will die in his 60th year? (Enter your answer to five decimal places.)Using this probability and the $50,000 death benefit, what is the expected cost to Big Rock Insurance? (Round your answer to two decimal places.)$ (b) Repeat part (a) for years 61, 62, 63, and 64. (Round your answers to two decimal places.) Year Expected Cost 61 $ 62 $ 63 $ 64 $ What would be the total expected cost to Big Rock Insurance…

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