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Q1 : Consider the following probability distribution function for a continuous random variable:
f(x) = 3x2 /35 -2< x < 3
= 0 elsewhere
(a) Show that this function satisfies the requirements of a probability distribution function.
(b) Calculate the expected (mean) value of x.
(c) Calculate the variance and the standard deviation of x.
Q2: In Problem 6.20, calculate the probability of the following cases:
(a) X ≤ 0.
(b) 0 < x ≤ 1.
(c) x = 2,
Q3: In the manufacturing of an electronic part, the probability of a part being defective is S% (a) What are the probabilities that, in a batch of 100 parts,
• 2 will be defective?• 5 will be defective?• 10 will be defective?
a report states that 57 of home owners had a vegetable garden. how large a sample is needed to estimate the true
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Paul received a score of 80 on a history test for which the class mean was 70 with a standard deviation of 10. He received a score of 75 on a biology test for which the class mean was 70
Based on p=.60, probability that a randomly selected homeowners will say no to newspaper subscription.
Use an appropriate 95 percent confidence interval to estimate the difference between the mean prices of the two brands of cd players. Do you think that the difference haspractical importance?
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Convinving evidence at the .05 significance level to support the claim that the actual number of cards is an undergrads wallet is greater than 4.09. state the null and alternative hypothesis.
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