The probability that a certain kind of component will survive a shock test is .8. 1. Find the probability that exactly 2 of the next 6 components you test will survive. 2. What is the probability that...
The probability that a certain kind of component will survive a shock test is .8.
1. Find the probability that exactly 2 of the next 6 components you test will survive.
2. What is the probability that you must test 8 components to find two that fail?
3. What is the probability that the 4th component you test is the first one that fails the test?
4. Out of a group of 100 components, 20 would fail a shock test. If you choose 10 components at random, what is the probability that you have exactly 2 that fail?
5. We mix into the group of components a third possibility--that the component fails to respond at all when tested--similar to a dead battery. Out of the 100 components, 70 are good, 10 are 'dead' and the other 20 would fail the shock test. You choose 10 at random. What is the probability that, of the 10, 7 are good, 1 is dead and the other 2 fail the shock test?
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The probability that a certain kind of component will survive a shock test is .8. 1. Find the probability that exactly 2 of the next 6 components you test will survive. 2. What is the probability that...
Problem 4: (2 points) A life test is performed on 10 components. The hours to failure...
Problem 4: (2 points) A life test is performed on 10 components. The hours to failure are as follows: 200 370 500 620 730 840 950 1050 1160 400 Assume this data follows a 2-parameter Weibull distribution. If an identical component is put on test and survives for 100 hours, what is the probability that it will survive for 200 additional hours?
6. The probability density function of (lifetime of an electronic component in years) X is f, (x)...
6. The probability density function of (lifetime of an electronic component in years) X is f, (x)- 4 x exp(-r)U(x) 32 (a) What value of A will make this a valid pdf? (b) What is the probability that it will fail within 6 years, given that normally these units tend to fail within 4 to7 years? (c) What is P[IX-316)? (d) If the unit is known to fail within 6-8 years, what is the probability that it fail within 7...
2. A certain type of electronic component has a lifetime X (in hours) with probability density...
2. A certain type of electronic component has a lifetime X (in hours) with probability density function given by otherwise. where θ 0. Let X1, . . . , Xn denote a simple random sample of n such electrical components. . Find an expression for the MLE of θ as a function of X1 Denote this MLE by θ ·Determine the expected value and variance of θ. » What is the MLE for the variance of X? Show that θ...
1. A student asks her teacher "What is the probability that it will take you exactly...
1. A student asks her teacher "What is the probability that it will take you exactly 20 minutes to walk to school in the morning?" What will be the teacher's reply? What is a better question to ask? Explain by referring to concepts that we discussed in this unit. 2. Describe how calculating probability for continuous random variables is different than calculating probability for discrete random variables. Explain using examples discussed in the activity and ideas discussed in this unit....
(d) What is the probability that at least two players receive exactly two hearts? 7. A...
(d) What is the probability that at least two players receive exactly two hearts? 7. A hand of 6 cards is drawn from a standard 52 card deck. (a) What is the probability of getting three different pairs? (ex: aabbcc) (b) What is the probability of getting two pairs? (ex: aabbcd) (c) What is the probability of getting three of a kind? (ex: aaabcd) (d) What is the probability of getting all cards with the same suit? 8. A bag...
1. Given below are marks obtained by 20 students out of 25 in Mathematics test. 21...
1. Given below are marks obtained by 20 students out of 25 in Mathematics test. 21 23 19 17 12 15 15 17 17 19 23 23 21 21 25 25 21 19 19 19 Calculate: i. measures of central tendency. (9 marks) ii. range and semi inter-quartile range. (6 marks) iii. variance and determine the shape of skewness. (5 marks) (b) A factory produces components of which 1% is defective. The components are packed in boxes of 10. A...
1. A certain medical test is known to detect 72% of the people who are afflicted...
1. A certain medical test is known to detect 72% of the people who are afflicted with the disease Y. If 10 people with the disease are administered the test, what is the probability that the test will show that: All 10 have the disease, rounded to four decimal places? .0374 At least 8 have the disease, rounded to four decimal places? At most 4 have the disease, rounded to four decimal places? Please show the steps in Microsoft excel...
Part I. Understanding What Makes an Experiment 1) Please identify the 3 vital components of an experiment. After identifying each component, write at least one sentence elaborating on/explaining each...
Part I. Understanding What Makes an Experiment 1) Please identify the 3 vital components of an experiment. After identifying each component, write at least one sentence elaborating on/explaining each component (10 points) Answer – The most conventional type of experiment involves three major pairs of components: independent and dependent variables, pretesting and post testing, and experimental and control groups. An experiment examines the effects of independent variable on a dependent variable. 1- Manipulate at least one independent variable. This means...
X1-X2-10 24. Consider the test HoHa-μ2-10 vs. μι-μ2 > 10 using the test statistic z-1-2 n1...
X1-X2-10 24. Consider the test HoHa-μ2-10 vs. μι-μ2 > 10 using the test statistic z-1-2 n1 n2 Suppose throughout that σ1-15 and σ2 20. a) Find the p-value if X1 -145.8 based on 50 samples and X2 -130.1 based on 50 samples b) Assume that the significance level of the test is 0.03. What is the conclusion?If it turns out that the conclusion was an error, is it a type I or type II error? c) Assuming the significance level...
Problem 4: (2 points) A life test is performed on 10 components. The hours to failure are as follows: 200 370 500 620 730 840 950 1050 1160 400 Assume this data follows a 2-parameter Weibull distribution. If an identical component is put on test and survives for 100 hours, what is the probability that it will survive for 200 additional hours?
6. The probability density function of (lifetime of an electronic component in years) X is f, (x)- 4 x exp(-r)U(x) 32 (a) What value of A will make this a valid pdf? (b) What is the probability that it will fail within 6 years, given that normally these units tend to fail within 4 to7 years? (c) What is P[IX-316)? (d) If the unit is known to fail within 6-8 years, what is the probability that it fail within 7...
2. A certain type of electronic component has a lifetime X (in hours) with probability density function given by otherwise. where θ 0. Let X1, . . . , Xn denote a simple random sample of n such electrical components. . Find an expression for the MLE of θ as a function of X1 Denote this MLE by θ ·Determine the expected value and variance of θ. » What is the MLE for the variance of X? Show that θ...
1. A student asks her teacher "What is the probability that it will take you exactly 20 minutes to walk to school in the morning?" What will be the teacher's reply? What is a better question to ask? Explain by referring to concepts that we discussed in this unit. 2. Describe how calculating probability for continuous random variables is different than calculating probability for discrete random variables. Explain using examples discussed in the activity and ideas discussed in this unit....
(d) What is the probability that at least two players receive exactly two hearts? 7. A hand of 6 cards is drawn from a standard 52 card deck. (a) What is the probability of getting three different pairs? (ex: aabbcc) (b) What is the probability of getting two pairs? (ex: aabbcd) (c) What is the probability of getting three of a kind? (ex: aaabcd) (d) What is the probability of getting all cards with the same suit? 8. A bag...
1. Given below are marks obtained by 20 students out of 25 in Mathematics test. 21 23 19 17 12 15 15 17 17 19 23 23 21 21 25 25 21 19 19 19 Calculate: i. measures of central tendency. (9 marks) ii. range and semi inter-quartile range. (6 marks) iii. variance and determine the shape of skewness. (5 marks) (b) A factory produces components of which 1% is defective. The components are packed in boxes of 10. A...
X1-X2-10 24. Consider the test HoHa-μ2-10 vs. μι-μ2 > 10 using the test statistic z-1-2 n1 n2 Suppose throughout that σ1-15 and σ2 20. a) Find the p-value if X1 -145.8 based on 50 samples and X2 -130.1 based on 50 samples b) Assume that the significance level of the test is 0.03. What is the conclusion?If it turns out that the conclusion was an error, is it a type I or type II error? c) Assuming the significance level...
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