Question

Problem 2 15 pts) Let the expected value of wind speed at 10 meters height be: $$\mathcal{E}(V_{10}) = \int_{-\infty}^{\infty} v_{10}f_{V_{10}}(v_{10}) dv_{10}$$ where $f_{V_{10}}$ is the probability density function of wind speed observed at 10 meters heigth. If the wind speed at height $h$ is $v_h = v_{10} (\frac{h}{10})^a$, what is the expected value of $v_h$ or simply $\mathcal{E}(V_h)$ in terms of $\mathcal{E}(V_{10})$? Hint: Let $X$ a random variable with probability density function $f_X$. Also, let $q: \mathbb{R} \mapsto \mathbb{R}$ a real-value function. The expectation $\mathcal{E}$ of $q(X)$ is: $$\mathcal{E}(q(X)) = \int_{-\infty}^{\infty} q(x) f_X(x) dx$$

          Problem 2 15 pts) Let the expected value of wind speed at 10 meters height be:
$$\mathcal{E}(V_{10}) = \int_{-\infty}^{\infty} v_{10}f_{V_{10}}(v_{10}) dv_{10}$$
where $f_{V_{10}}$ is the probability density function of wind speed observed at 10 meters heigth.
If the wind speed at height $h$ is $v_h = v_{10} (\frac{h}{10})^a$, what is the expected value of $v_h$ or simply $\mathcal{E}(V_h)$ in terms of $\mathcal{E}(V_{10})$?
Hint: Let $X$ a random variable with probability density function $f_X$. Also, let $q: \mathbb{R} \mapsto \mathbb{R}$ a real-value function. The expectation $\mathcal{E}$ of $q(X)$ is:
$$\mathcal{E}(q(X)) = \int_{-\infty}^{\infty} q(x) f_X(x) dx$$

problem 2 15 pts let the expected value of wind speed at 10 meters height be mathcalev10 int inftyinfty v10fv10v10 dv10 where fv10 is the probability density function of wind speed 35746

Added by Jonathan A.

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