Probability and Statistics

Question 8: The current advertising campaign for a major soft drink brand would be changed if less than 30 percent of consumers like it. a) Formulate the null and alternative hypothesis b) Discuss the Type land Type II errors that could occur in hypothesis testing. c) Which statistical test would you use? Why? d) A random sample of 300 consumers was surveyed, and 84 respondents indicated that they liked the campaign. Should the campaign be changed? Why?

EXPERT ANSWER a) Ho : p = 0.3H1 : p < 0.3 b) Type I error is concluding that less than 30% of custimers like it while in actual it equal or greater than 30% Type I error is concluding that equal to or greater than 30% of custimers like it while in actual it …

Question 8: The current advertising campaign for a major soft drink brand would be changed if less than 30 percent of consumers like it. a) Formulate the null and alternative hypothesis b) Discuss the Type land Type II errors that could occur in hypothesis testing. c) Which statistical test would you use? Why? d) A random sample of 300 consumers was surveyed, and 84 respondents indicated that they liked the campaign. Should the campaign be changed? Why? Read More »

Q4) At a county fair, a ring toss game may be played for 25 cent. You are given three rings and then attempt to toss them individually onto a peg. If you successfully get one ring on a peg, you win a prize worth 50 cents. If you get two on, you get a prize worth 1 dollar and if you get all three on, you win a prize worth 5 dollars. Assuming the probability that you ring the peg is 0.1 each try, a) Find the probability mass function of your gain if you play this game one time. b) What is your expected gain if you play this game one time? c) What is your expected gain if you play this game ten times?

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(a) The periodic signal given in 1. (a) can be represented as a trigonometric Fourier series: f(t)= n=−∞ ∑ ∞ ​ C n ​ e jnω 0 ​ t , where ω 0 ​ = T 0 ​ 2π ​ . (i) Write an expression for C n ​ . (ii) For a certain periodic function p(t) , the magnitude spectrum and the phase spectrum for C n ​ are given below: 1. What is the distance between 2 consecutive spectral lines? 2. Sketch ∣C n ​ ∣ and ∠C n ​ for the function p(t−t 0 ​ )

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A manufacturer makes ball bearing that are supposed to have a mean weight of 30 g. A retailer suspects that the mean weight is actually less than 30g the mean weight for a random sample of 16 ball bearings is 28.6 g with a standard deviation of 4.4 g. At the 0.05 significance level these the claim that the sample comes from a population with a mean weight less than 30 g. Use the traditional method of testing hypothesis.

A manufacturer makes ball bearing that are supposed to have a mean weight of 30 g. A retailer suspects that the mean weight is actually less than 30g the mean weight for a random sample of 16 ball bearings is 28.6 g with a standard deviation of 4.4 g. At the 0.05 significance level these …

A manufacturer makes ball bearing that are supposed to have a mean weight of 30 g. A retailer suspects that the mean weight is actually less than 30g the mean weight for a random sample of 16 ball bearings is 28.6 g with a standard deviation of 4.4 g. At the 0.05 significance level these the claim that the sample comes from a population with a mean weight less than 30 g. Use the traditional method of testing hypothesis. Read More »

4. (15 points) When a fair coin is tossed, 2 points are scored if a head is obtained and 5 points are scored if a tail is obtained. Suppose the coin is tossed three times and let the random variable X be the total score obtained. (a) What are the possible values of X? (b) What is the probability mass function of X? (c) What is the cumulative distribution function of X? (d) What is the expected value and standard deviation of X?

EXPERT ANSWER Q4) a) X is the total number of points that can be obtained here. There are 4 possible combinations here for 3 tosses:All heads where we get: 3*2 = 6 points2 heads and 1 tails: 2*2 + 5 = 9 points1 head and 2 tails: 2 + 5*2 = 12 points3 tails: 15 …

4. (15 points) When a fair coin is tossed, 2 points are scored if a head is obtained and 5 points are scored if a tail is obtained. Suppose the coin is tossed three times and let the random variable X be the total score obtained. (a) What are the possible values of X? (b) What is the probability mass function of X? (c) What is the cumulative distribution function of X? (d) What is the expected value and standard deviation of X? Read More »

4.6 XR04-06 The mid-semester exam marks (marked out of 30) in a finance course are as follows: 17 11 6 21 25 21 8 17 22 19 18 19 14 6 21 20 25 19 9 12 16 16 10 29 24 a Construct a frequency distribution for these data. Use five class intervals, with the lower boundary of the first class being five marks. b Construct a relative frequency histogram for these data, What is the relationship between the areas under the histogram you have constructed and the relative frequencies of observations? C

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6. A black and White picture can be thought of as being composed of a large number of picture elements with each picture element taking on a grey level. Assume that each picture element is square and is 10-4 meters on the side. Also assume that each picture can take on one of eight equally likely values and that all picture elements are statistically independent. How much information is in a square with a side dimension of 10-2 meters?

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The following profit payoff table was presented in Problem 1. Suppose that the decision maker obtained the probability assessments P(s1) 5 0.65, P(s2) 5 0.15, and P(s3) 5 0.20. Use the expected value approach to determine the optimal decision.

The following profit payoff table was presented in Problem 1. Suppose that the decision maker obtained the probability assessments P(s1) 5 0.65, P(s2) 5 0.15, and P(s3) 5 0.20. Use the expected value approach to determine the optimal decision. State of NatureDecision Alternative s1 s2 s3d1 250 100 25 d2 100 100 75 EXPERT ANSWER