Let the probability density of continuous random variable X be f (x) = {SiNx, 0 ≤ x ≤ a (previous line) 0, others (next line after braces). Try to determine the constant a and find P (x > π / 6)

Let the probability density of continuous random variable X be f (x) = {SiNx, 0 ≤ x ≤ a (previous line) 0, others (next line after braces). Try to determine the constant a and find P (x > π / 6)

F(+oo)=int(-oo,+oo)f(x)dx=int(0,a)sinxdx=1-cosa=1
cosa=0,a=2π
P = 1-f (π / 6) = 1-int (0, π / 6) sinxdx = radical 3 / 2