A random process has the power density spectrum Sxx(@) = %3D 1+ m2" Find the average power in the process.
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- Later, when the medical devices are in full production, a consultant advised that the breaking strength of these devices should not be less than 5.5 psi (pounds per square inch) on average. In the latest batch produced, a technician has noticed a visual defect that may affect the breaking strength of the devices. To investigate, a sample of 8 devices are randomly selected from the batch and the pressure at which they break are recorded as : 6.6, 7.7, 8.0, 6.3, 6.1, 6.3, 6.3, 6.1 these are summarized as having an average breaking strength of 6.68 psi and a standard deviation of s = 0.75 psi. Test, at significance level α = 0.05, whether there is evidence that the average breaking strength of the batch of devices is less than the required breaking strength, by testing the hypotheses: H 0: μ = 5.5 psi H a: μ < 5.5 psi. An estimate of the population mean is . The standard error is . The distribution is (examples: normal / t12 / chisquare4 / F5,6). The test statistic has value TS=…A. The approximate standard deviation for the area under a gaussian curve for a population in the figure is .........The total area under the curve is 1 b) If 3% of electric bulbs manufactured by a company are defective find the probability that a sample of 100 bulbs will contain: No defective bulb
- If a dealer’s profit, in units of $5000, on a new automobile can be looked upon as a random variable X having the density function Find the variance of X.The probability density function of the random variable X is as in the picture with λ> 0. Find the moments estimator (λ^) of the parameter λ.Demonstrate the density function of the continuous uniform distribution from the data presented in the image.
- Suppose that the lifetime X (in hours) of a certain type of flashlight battery is a random variable on the interval 30 ≤ x ≤ 50 with density function f(x) = 1/20, 30 ≤ x ≤ 50. Find the probability that a battery selected at random will last at least 35 hours.In kurtosis, the bell shaped distribution called mesokurtic if the frequency looks more peaked than normal. True or false?The probability density function of the random variable X is as in the picture with λ> 0. Find the maximum likelihood estimator (λ^) of the parameter λ.
- The molecular weight of a particular polymer should fall between 750 and 1,035. Thirty samples of this material were analyzed with the results X-bar = 902 and s = 90. Assume that molecular weight is normally distributed.A discrete random variable X has probability mass function X 0 1 2 3 4 P(x) 0.1 0.2 0.2 0.2 0.3 Use the inverse transform method to generate a random sample of size 1000 from the distribution of X. Construct a relative frequency table and compare with the theoretical values.If X has a uniform density with α = 0 and β = 1, show that the random variable Y = −2. In X has a gamma dis-tribution. What are its parameters?
