Question

3. Let X be a random variable with the following density function: $f(x) = \begin{cases} \frac{x}{2} & \text{if } 0 \le x \le 2\\ 0 & \text{elsewhere} \end{cases}$ and given X, $f(y|x) = \begin{cases} Ce^{-(y-12x)^2} & \text{if } -\infty < y < \infty\\ 0 & \text{elsewhere} \end{cases}$ Find EY.

          3. Let X be a random variable with the following density function:
\(f(x) = \begin{cases} \frac{x}{2} & \text{if } 0 \le x \le 2\\ 0 & \text{elsewhere} \end{cases}\)
and given X,
\(f(y|x) = \begin{cases} Ce^{-(y-12x)^2} & \text{if } -\infty < y < \infty\\ 0 & \text{elsewhere} \end{cases}\)
Find EY.

3. Let X be a random variable with the following density function:
f(x) = (x)/(2) if 0 ≤ x ≤ 2
0 elsewhere
and given X,
f(y|x) = Ce^-(y-12x)^2 if -∞ < y < ∞
0 elsewhere
Find EY.

Added by Aaron W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Jainendra Ojha

Step 1

The marginal density of $X$ is: \[ f(x) = \frac{x}{2} \quad \text{for } 0 \le x \le 2 \] The conditional density of $Y$ given $X$ is: \[ f(y|x) = Ce^{-(y-12x)^2} \] Show more…

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3. Let X be a random variable with the following density function: $$f(x) = \begin{cases} \frac{x}{2} & \text{if } 0 \le x \le 2 \\ 0 & \text{elsewhere} \end{cases}$$ and given X, $$f(y|x) = \begin{cases} Ce^{-(y-12x)^2} & \text{if } -\infty < y < \infty \\ 0 & \text{elsewhere} \end{cases}$$ Find EY.