Question

Wind speed $v(t)$ at a given location approximates a Rayleigh distribution, with probability density function given by $p(v) = frac{v}{v_0^2} expleft(-frac{v^2}{2v_0^2} ight)$ for $v ge 0$, with $v_0 = 5 ext{ m s}^{-1}$. (a) Estimate the probability of the windspeed being more than $10 ext{ m s}^{-1}$ at any given time. (b) Estimate the 99th percentile of windspeed (that is, a speed that is exceeded 1% of the time). (c) Estimate the average value of $v^3$. This is important for planning wind power facilities, since the power available is proportional to $v^3$.

          Wind speed $v(t)$ at a given location approximates a Rayleigh distribution, with probability density function given by

$p(v) = frac{v}{v_0^2} expleft(-frac{v^2}{2v_0^2}
ight)$

for $v ge 0$, with $v_0 = 5 	ext{ m s}^{-1}$.
(a) Estimate the probability of the windspeed being more than $10 	ext{ m s}^{-1}$ at any given time.
(b) Estimate the 99th percentile of windspeed (that is, a speed that is exceeded 1% of the time).
(c) Estimate the average value of $v^3$. This is important for planning wind power facilities, since the power available is proportional to $v^3$.

$Wind speed v(t) at a given location approximates a Rayleigh distribution, with probability density function given by p(v) = fracvv0^2 expleft(-fracv^22v0^2 ight) for v ge 0, with v0 = 5 ext m s^-1. (a) Estimate the probability of the windspeed being more than 10 ext m s^-1 at any given time. (b) Estimate the 99th percentile of windspeed (that is, a speed that is exceeded 1% of the time). (c) Estimate the average value of v^3. This is important for planning wind power facilities, since the power available is proportional to v^3.$

Added by Jessica Z.

Question

Please give Ace some feedback