Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.

In 2017, the entire fleet of light‑duty vehicles sold in the United States by each manufacturer must emit an average of no more than 9090 milligrams per mile (mg/mi) of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) over the useful life (150,000150,000 miles of driving) of the vehicle. NOX ++ NMOG emissions over the useful life for one car model vary Normally with mean 8484 mg/mi and standard deviation 66 mg/mi. (a) What is the probability that a single car of this model emits more than 9090 mg/mi of NOX ++ NMOG? (Enter your answer rounded to four decimal places.) (b) A company has 1616 cars of this model in its fleet. What is the probability that the average NOX ++ NMOG level ?¯x¯ of these cars is above 9090 mg/mi? (Enter your answer rounded to four decimal places.)

Let Y be a random variable with the mgfM(t) = .35e^(−4t) + .1 + .25e^(2t) + .3e^(4t).(a) What is the pmf of Y?(b) Calculate the variance of Y directly from the pmf you determined in part (a).(c) Calculate E[Y^4] directly from the mgf.

Q13 b and c pls, thank you. Mean = 1/500 = 0.002var(x) = 1/500^2 = 0.000004