If X is a uniformly distributed continuous random variable with possible values in the interval [-3,5]
A)compute μx
B)compute σ^2X
C) Find P (|X| ≥ 1.5)

Question

If X is a uniformly distributed continuous random variable with possible values in the interval [-3,5]
A)compute μx
B)compute σ^2X
C) Find P (|X| ≥ 1.5)

anonymous · Answer

Since $X$ is uniformly distributed on $[-3,5]$, its probability density function is
$$f(x)=\begin{cases}
\dfrac{1}{5-(-3)}=\dfrac{1}{8}&\text{for }-3\le x\le5\
0&\text{otherwise}
\end{cases}$$
The mean $\mu$ is
$$E(X)=\int_{-\infty}^\infty f(x)~dx$$
and the variance $\sigma^2$ is
$$\begin{align*}
V(X)&=E(X^2)-[E(X)]^2\
&=\int_{-\infty}^\infty x^2~f(x)~dx-\mu^2
\end{align*}$$
For part (c), you're equivalently finding
$$P(|X|\ge1.5)=P(-1.5\ge X\text{ or }X\le1.5)=P(X\ge1.5)+P(X\le-1.5)$$
i.e. the total area of the shaded regions
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