20 The continuous random variable X has a pdf fy (x) = x/2, 0

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Answered: The continuous random variable X has a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A random sample X1, X2, ..., Xn is obtained for a random variable X believed to be distributed as Beta(a, 7) (notice that B = 7 is known). Use the method of moments to determine the value of given 0.72.
Suppose that Yis a continuous random variable, with Y ~ Normal(µ, o²) where the two parameters and take values 2 and 0.5 respectively. Using the table of the Normal distribution, compute P(Y > y) if y=1.608. Give your answer to 3 decimal places. Note that the Normal table can be used for arguments specified up to two decimal places, so round your arguments appropriately.
Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.
Let X~Geo(0.3). Find the following a. P(X = k). b. P(1 ≤ X 3) and describe its interpretation. d. The mean μ = E(X) and the Variance σ2 = Var (X) of the random variable X.
The pressure of air (in MPa) entering a compressor is measured to be X = 8.5 ± 0.2, and the pressure of the air leaving the compressor is measured to be Y = 21.2 ± 0.3. The intermediate pressure is therefore measured to be P = √XY = 13.42 . Assume that X and Y come from normal populations and are unbiased. a) From what distributions is it appropriate to simulate values X* and Y*? b) Generate simulated samples of values X*, Y*, and P*. c) Use the simulated sample to estimate the standard deviation of P. d) Construct a normal probability plot for the values P*. Is it reasonable to assume that P is approximately normally distributed? e) If appropriate, use the normal curve to find a 95% confidence interval for the intermediate pressure.
The average wait time to get seated at a popular restaurant in the city on a Friday night is 12 minutes. Is the mean wait time greater for men who wear a tie? Wait times for 13 randomly selected men who were wearing a tie are shown below. Assume that the distribution of the population is normal. 13, 13, 11, 13, 13, 13, 13, 10, 12, 13, 13, 10, 13 What can be concluded at the the αα = 0.05 level of significance level of significance? The null and alternative hypotheses would be: H0 = (p,u) (<,>,=,not equal) to _____ H1 = (p,u) (<,>,=,not equal) to _____ The test statistic (t,z) = ___ The p-value = _____ Thus, the final conclusion is that ... The data suggest that the population mean wait time for men who wear a tie is not significantly more than 12 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean wait time for men who wear a tie is more than 12. The data suggest the population mean is not significantly more than 12…
A variable X has a probability function f(x, 0) = 0e 0x; x≥0 y >0. The parameter 0 is estimated using two different estimators of simple random samples of size two: 01 2x+4x2 and 2=4x+5x2 3 3 Select the best estimator for \theta by comparing the Mean Squared Errors
Let X be a continuous random variable that is normally distributed with mean, µ = 15 and standard deviation, o = 2.8, find a value xo that represents the 80th percentile of the distribution. Answer should be accurate to two decimal places.

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