Question

if x ~ u(3,7), then p(x = 4) = p(x = 9)
false
true

Explanation:

Step1: Recall uniform - distribution property

For a continuous uniform distribution $X\sim U(a,b)$ with $a = 3$ and $b = 7$, the probability density function is $f(x)=

$$\begin{cases}\frac{1}{b - a},&a\leq x\leq b\\0,&\text{otherwise}\end{cases}$$

$. Here, $f(x)=\frac{1}{7 - 3}=\frac{1}{4}$ for $3\leq x\leq7$ and $0$ otherwise.

Step2: Analyze point - probabilities

In a continuous distribution, the probability of a single point is $0$. That is, for any $x_1,x_2$ in the domain or outside the domain of the continuous uniform distribution, $P(X = x_1)=P(X = x_2)=0$. Since $4\in[3,7]$ and $9
otin[3,7]$, $P(X = 4)=0$ and $P(X = 9)=0$.

Answer:

true