Calculate xpectation and variance of X, if the probability distribution of the random variable X is given by X - 1 0.3 0 0.1 I 0.1 2 3 0.3 0.2
Q: The joint probability distribution of two random variables X, Y is given in the table below. Y=-4…
A: y=-4 y=-2 y=0 y=2 y=4 total x=0 0.02 0.07 0.11 0.03 0.08 0.31 x=2 0.00 0.11 0.09 0.12 0.00…
Q: 2. Let X be a random variable with the following probability distribution: -4 1 P(X)| 0.2 0.3 0.4…
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Q: The joint probability distribution of two random variables X, Y is given in the table below. Value…
A: The marginal density function of X is X -3 3 4 P(X) 0.35 0.32 0.33 The marginal density…
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A: Given, a probability distribution Then , mean = Ex = ∑x=04x fx Variance= Ex2 - Ex2where Ex2…
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A: Given data is x 3 4 5 6 p(x) 0.45 0.25 0.15 0.15
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A: Rules of probability distribution: The probability values of each value of x should be between 0 to…
Q: The joint probability distribution of two random variables X, Y is given in the table below. Value…
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Q: The joint probability distribution of two random variables X, Y is given in the table below. Value…
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Q: If X is a Poisson random variable with a rate of 5. Then, Calculate the probability P( X < 2)?
A: The probability mass function of a Poisson distribution with rate parameter P(X=k)=e-λ·λkk! where λ…
Q: The joint probability distribution of two random variables x, Y is given in the ta below. Y=-2 Y=- 1…
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Q: 3. Let X be a random variable with the following probability distribution: 5 10 15 20 25 X P(X) 0.5…
A: X 5 10 15 20 25 P(X) 0.5 0.30 0.25 0.25 0.15
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Q: The joint probability distribution of two random variables X, Y is given in the table below. Y=-3…
A: Solution-: From given joint probability distribution table of two random variables X and Y we find,…
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Q: Y=-2 Y=-1 Y 1 Y=2 Y=3 X=-3 0.00 0.01 0.00 0.03 0.19 X=-2 0.07 0.00 0.13 0.01 0.10 X=0 0.00 0.03 0.20…
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Q: local teacher is interested in genealogy and decides to collect data from her co : her school know…
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Q: Suppose X is a random variable with the following distribution: xi 1 2 5 10 pi 0.4 0.3 0.2…
A: the expected value of X is given by the formula EX=∑ixipi substitute the values…
Q: The joint probability distribution of two random variables X, Y is given in the table below. Y=-4…
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Q: The joint probability distribution of two random variables X, Y is given in the table below. Y=-2…
A: For Y=2 Probabilities are given for every X, i.e. 0.04, 0.19, 0.05 So P(Y=2)= 0.04+0.19+0.05= 0.28
Q: The joint probability distribution of two random variables X, Y is given in the table below. Y=-3…
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Q: Suppose X is a discrete random variable with the following probability distribution: P(X = 2) = 0.3…
A: Given information P(X = 2) = 0.3, P(X = 4) = 0.2,P(X = 6)=0.5
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Q: Let X be a random variable that can take the values 5, 9, or 13. And let f(x) be its probability…
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Q: Find the variance and standard deviation of X
A: The variance can be calculated as V(X) = E(X2) - [E(X)]2
Q: (a) P(Y z 2) = [] (b) P(X< 1,Y = 2) = [ (c) P(Y< -3) = [O
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Q: Let X be a random variable with range {20,30,50} and probability distribution P(X=20) = 0.25,P(X=30)…
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Q: The Poisson and Gaussian probability distributions of a random variable x assume a similar shape as…
A: The Poisson and Gaussian probability distributions of a random variable x assume a similar shape as…
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- An infectious flu virus is spreading through a school. The probability of a randomly selected student having the flu next week is 0.3. Mr C has a class of 20 students. (i)Name a suitable probability distribution to model variable X, stating the parameters. (ii) Calculate the probability that 2 or more students will have the flu next week. (iii) If more than 20% of the students have the flu next week, a class test will have to be cancelled. What is the probability that the test will be cancelled? (iv) If the school has 350 students, find the expected number that will have the flu next weekLet X be a random variable that can take the values 2, 9, or 13. And let f(x) be its probability distribution. Find the variance of the random variable X, given that its probability distribution is f(2) = 0.1 f(9) = 0.4 f(13) = 0.5 Round your answer to an integer.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…
- A small ferry runs every half hour from one side of a large river to the other. The probability distribution for the random variable Y = money collected (in dollars) on a randomly selected ferry trip is shown here. Money collected Probability P(Y ≤ 0) = 0 Incorrect 0.02 5 0.05 10 0.08 Calculate the cumulative probabilities. Do not round. 15 0.16 20 0.27 25 0.42 P(Y <5)= IncorrectA company has seven applicants for two positions: three women and four men. Suppose that the seven applicants are equally qualified and that no preference is given for choosing either gender. Let x equal the number of women chosen to fill the two positions. (a) Write the formula for p(x), the probability distribution of x. (b) What are the mean ? and variance ?2 of this distribution? (Round your mean to one decimal place and your variance to two decimal places.)Suppose that for a given computer salesperson, the probability distribution of x the number of systems sold in 1 month is given by the following table. 1 2 3 4 8. P(x) 0.05 0.10 0.12 0.30 0.30 0.11 0.01 0.01 (a) Find the mean value of x (the mean number of systems sold). (b) Find the.variance and standard deviation of x. (Round your standard deviation to four decimal places.) variance standard deviation How would you interpret these values? (Round your standard deviation to four decimal places.) The mean squared deviation from the mean number of systems sold in one month is A typical deviation from the mean number of systems sold in one month is (c) What is the probability that the number of systems sold is within 1 standard deviation of its mean value? 1. (d) What is the probability that the number of systems sold is more than 2 standard deviations from the mean?
- A company that sells binders decides to run a promotion on their 1-inch and 2-inch size binders. Theydiscount the 1-inch binders to $1 per binder and discount the 2-inch binders to $2 per binder. They limitsales to a quantity of 5 of each size of binder per customer. The probability distribution of “X = the numberof 1-inch binders purchased by a single customer during the promotion period” is given in the table below. X 1 2 3 4 5 P(X) 0.02 0.09 0.12 0.15 0.62 a) Compute the mean and standard deviation of X. b) The company’s cost of manufacturing a single 1-inch binder is $0.25. What is the expected profit (indollars) that the company will make, per customer, for 1-inch binder sales during the promotion? c) The mean and standard deviation of “Y = the number of 2-inch binders purchased by a singlecustomer” is 2.74 and 1.25, respectively. Assume that the number of 1-inch and 2-inch binderspurchased are independent random variables. What are the mean and standard deviation of the…random variable, y, has a known probability distribution given by Y :2,4,6,8,10 and P 0.17.0.23, 0.2.0.3.0.1 the expected value of y is 5 O a. True Ob. FalseOxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was μ = 9.2 mg/L with 95% of the data ranging from 5.4 mg/L to 13.0 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume xhas a probability distribution that is approximately normal. (a) Use the 95% data range to estimate the standard deviation for oxygen demand. (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L?(Round your answer to four decimal places.) (c) A high oxygen demand can also indicate trouble. An oxygen demand above 12 may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12…
- Two six-sided dice are rolled and the random variable x is the sum of the values produced by each die. a. List the possible outcomes for the variable x, determine the probability for each outcome, and calculate the expected value of x. b. Calculate the variance of x. c. Calculate the standard deviation of x. a. List the possible outcomes for the variable x. Choose the correct answer below. O A. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 О В. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ОС. 1,2, 3, 4, 5, 6 O D. 3, 4, 5, 6, 7, 8, 9, 10, 11 Determine the probability for each outcome. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or fractions.) O A. P(1) =. P(2) = P(3) = P(4) = P(5) = P(6) = О В. Р/2)- P(3) = , P(4) = , P(5) = P(6) = P(7) = P(8) = P(9) = , P(10)= P(11) = P(12) = %3D O C. P(3) = P(4) = , P(5) = , P(6) = ,P(7) = P(8) = P(9) = P(10) = P(11) = O D. P(1)= , P(2) = , P(3) = P(4) = , P(5) = P(6) = P(7) = P(8) = P(9) = P(10) = P(11) = P(12)…A discrete random variable can assume 5 possible values, as listed in the accompanying probability distribution. x: -5 0 2 5 p(x): 0.20 0.30 0.10 (c) Find the variance of x.The joint probability distribution of two random variables X, Y is given in the table below. Y=-4 Y=0 Y=1_Y=4 X=-4 0.01 0.18 0.00 0.13 X=-1 0.03 0.08 0.20 0.14 X=4 0.00 0.08 0.09 0.06 From the information in the table, calculate each of the following three probabilities. (a) P(Y= -4) = | (b) Р (х < -1, ү 2 0) %3D0 (c) P(x< 5) = []