Question

the probability distribution of a random variable x is given in the figure below.
from this distribution, the probability that x is at least 0.52 is:
give your answer to at least 4 decimal places.

Explanation:

Step1: Identify the distribution type

Assume it's a uniform distribution on $[0, 2]$. The probability - density function of a uniform distribution $U(a,b)$ is $f(x)=\frac{1}{b - a}$ for $a\leq x\leq b$ and $0$ otherwise. Here, $a = 0$ and $b = 2$, so $f(x)=\frac{1}{2-0}=\frac{1}{2}=0.5$ for $0\leq x\leq 2$.

Step2: Calculate the probability

The probability $P(X\geq0.52)$ for a continuous - uniform distribution is calculated using the formula $P(X\geq x)=\frac{b - x}{b - a}$. Substitute $a = 0$, $b = 2$, and $x = 0.52$ into the formula. Then $P(X\geq0.52)=\frac{2 - 0.52}{2-0}=\frac{1.48}{2}=0.7400$.

Answer:

$0.7400$