Power meters enable cyclists to obtain power measurements nearly continuously. The meters also calculate the average power generated over a time interval. Professional riders can generate 6.6 watts per kilogram of body weight for extended periods of time. Some meters calculate a normalized power measurement to adjust for the physiological effort required when the power output changes frequently. Let the random variable X denote the power output at a measurement time and assume that X has a lognormal distribution with parameters θ = 5.2933 and ω² = 0.00995. The normalized power is computed as the fourth root of the mean of Y = X⁴.

Determine the following:

(a) Mean and standard deviation of X

(b) f_Y (y)

(c) Mean and variance of Y

(d) Fourth root of the mean of Y

(e) Compare [E(X⁴)]^1/4 to E(X) and comment.