Show that for the Gamma distribution e*x dp = 14. dx, 0
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample?Show that a gamma distribution with α > 1 has a rel-ative maximum at x = β(α − 1). What happens when 0 <α< 1 and when α = 1?
- Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample? I asked this question earlier today, but didn't quite understand all of the response. P(y1<=yn)p(y2<=yn) and so on was used, but shouldn't the yn be listed first in the inequality since we want to know if yn is the smallest?Suppose that Y has an exponential distribution with mean Beta. Show that 2Y/Beta has a chi square distribution with 2 degrees of freedom.1. Let X have a gamma distribution with α > 1. Show thatE [1/X] = 1/[θ*(α −1)]
- Suppose that X has a lognormal distribution with parameters θ = 5 and ω2 = 9. Determine the following: a. P(X < 13,300)b. Value for x such that P(X ≤ x) = 0.95c. Mean and variance of XFind the mean and variance of the gamma distributionusing integration to obtain E(X) and E(X2).[Hint: Express the integrand in terms of a gammadensity.]1. Consider the Gaussian distribution N (m, σ2).(a) Show that the pdf integrates to 1.(b) Show that the mean is m and the variance is σ.
- If the probability mass function of the variable X described in the table is. find variance Y=x^2+4x If you know that the torque is of the second order of the variable X about the origin is equal to 2.85find the z-score that has 30.5 of the distribution's area to its leftsolve the problem in the photo using normal distribution laws