Suppose that the probabilities are 0.2, 0.4, 0.3, and 0.1, respectively, that 0, 1, 2, or 3power failures will strike a certain subdivision in any given year. Find the mean andvariance of the random variable X representing the number of power failures striking thissubdivision.Calculate the mean, μ.The mean is (Round to two decimal places as needed.) Let X denote the number of times a certain numerical control machine will malfunction:1, 2, or 3 times on any given day. Let Y denote the number of times a technician iscalled on an emergency call. Their joint probability distribution is given in theaccompanying table. Determine the covariance between X and Y.Click the icon to view the joint probability distribution of X and Y.OXY =(Type an integer or a decimal. Do not round.)Machine Malfunctionsyf(x,y)13510.100.050.00X20.100.050.2530.050.350.05-X

The random variable X represents the number of power failure striking the subdivision.Hey there!…

Answered: Suppose that the probabilities are 0.2,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question 4 Let X be a discrete random variable with a binomial distribution. The mean of X is 20 and the variance is 12. The values of n (the number of independent trials) and p (the probability of each trial) are The mean of X is A. p = 50 and n = 0.4 B. p = 0.6 and n = 50 C. p = 0.2 and n = 100 D. p = 0.72 and n = 50 E. p = 0.4 and n = 50 Question 5 The random variable X has a normal distribution with a mean of 50 and a variance of 49. If the random variable Z has a standard normal distribution, the probability that X is greater than 71 is A. 1- Pr(Z 3) C. Pr(-3 < Z < 3) D. Pr(Z < 3) E. Pr(Z < -3)
Following is the probability distribution for the age of a student at a certain public high school. x 13 14 15 16 17 18 Px 0.08 0.23 0.22 0.29 0.14 0.04 Find the variance of the ages
. Given a normal random variable X with mean μ = 100 and variance o² = 49 if we randomly observe X=30, is this an unusual observation? (a) This would be an unusual observation because it lies less than 3 standard deviations away from the mean. (b) This would not be an unusual observation because it lies less than 3 standard deviations away from the mean. (c) This would be an unusual observation because it lies more than 3 standard deviations away from the mean. (d) This would not be an unusual observation because it lies more than 3 standard deviations away from the mean.
Suppose that X can only take on one of the 4 possible values from the probability distribution given below. What is the variance of X?(use a decimal number, rounded to the nearest 10th, without $ sign. For example, 1.2)
(Sec. 5.4) Let X denote the courtship time for a randomly selected female-male pair of mating scorpion flies. Suppose the mean value of X is 120 min. and the standard deviation of X is 110 min. (a) Is it plausible that X is normally distributed? Explain why or why not. (b) For a random sample of 55 such pairs, what is the approximate probability that the sample mean courtship time is between 100 min. and 125 min.? (c) For a random sample of 55 such pairs, what is the approximate probability that the total courtship time is greater than 150 hours?
The data on the right represent the number of live multiple-delivery births (three or more babies) in a particular year for women 15 to 54 years old. Use the data to complete parts (a) through (d) below. Age Number of Multiple Births 15-19 90 20-24 512 25-29 1633 30-34 2839 35-39 1842 40-44 379 45-54 115 (a) Determine the probability that a randomly selected multiple birth for women 15-54 years old involved a mother 30 to 39 years old. P(30 to 39)=0.6320.632 (Type an integer or decimal rounded to three decimal places as needed.) (b) Determine the probability that a randomly selected multiple birth for women 15-54 years old involved a mother who was not 30 to 39 years old. P(not 30 to 39)=nothing (Type an integer or decimal rounded to three decimal places as needed.)
Suppose you want to determine whether the average values for populations 1 and 2 are different, and you randomly gather the following data. Test your conjecture, using a probability of committing a Type I error of .01. Assume the population variances are the same and x is normally distributed in the populations. Sample 1: 2 10 7 8 2 5 9 1 8 0 2 8 11 2 4 5 3 9 Sample 2: 10 12 8 7 9 11 9 8 9 10 11 10 11 10 7 8 10 10 Find the t-score to make a conclusion. (Round your answer to 2 decimal places, e.g. 1.75. Enter negative amount using a negative sign preceding the number e.g. -1.75.) Observed t = Type your answer here The decision is to Choose your answer here fail to reject the null hypothes is reject the null hypothesis.
Question 6: If the random variable X has a normal distribution with mean 40 and std. dev. 5, calculate the following probabilities. Р(X > 43), P(X 23).
The mean height of 15-year-old boys (in em) is 175 and the variance is 64. For girls, the mean is 165 and the variance is 64. Assuming that the two populations are nomally distributed. If eight boys and eight girls were sampled, then the probability that the mean height of the sample of boys would be higher than the mean height of the sample of girls 18: O 0 9878 O 0.0062 O 0.9938 0 9972 Let E[X(Y-1)] 10, E[X(Y#1)] 20, V(X) Then E(Y) 8. V(Y) 12 and V(X+Y) 30. O 14/5 12/5 2
Suppose that for a given computer salesperson, the probability distribution of x = the number of systems sold in one week is given by the following table. x 1 p(x) 2 3 4 5 0.06 0.10 (a) Find the mean value of x (the mean number of systems sold). 0.11 0.30 6 7 8 0.29 0.12 0.01 0.01 (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 week is A typical deviation from the mean number of systems sold in one week is (c) What is the probability that the number of systems sold is within 1 standard deviation of its mean value? (d) What is the probability that the number of systems sold is more than 2 standard deviations from the mean?
Question 4. a. On a random day, a store can sell a mean value of 32 pasta packages and a standard deviation of 4. What is the probability that the total number of pasta packages sold by the store for a random sample of 58 days is less than 1862? Explain. Let b. X₁, X2, X3, and X4 represent the weight of shipment packages at a certain shipment facility. Suppose they are independent normal random variables with means M₁ = 0.8, M₂ = 2.6, μ3 = 8.4, µ4 = 2.3 pounds and variances . Find o² = 0² = 0} = 0} = 1 P(3X₁ + 1X2 + 1X3 + 2X4 ≤ 16.8)

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