Answer:
[tex]P(X>50)=0.5[/tex]
Step-by-step explanation:
The probability density function,[tex]f(x)[/tex], of a random variable X is defined as:-
[tex]\int\limits^a_b {x} \, dx[/tex]=[tex]\int\limits^{50.25}_{49.75} {2} \, dx[/tex]
To obtain P(X>50), we will integrate the function over the limits 50.25 and 50.0 as below:
[tex]\int\limits^{50.25}_{50.00} {2} \, dx \\=0.25*2\\=0.5[/tex]
Therefore, P(x>50) is true for any value of x that is greater than 50 and therefore P(X>50)=0.5
