If the error involved in making a certain measurement is continuous random variable X with probability density function f(x)=k (4-x² ) if -2 x 2=0 , otherwise then, P [-1 < X < 1]=

Step-by-step solution

Since the function represents a p.d.f. aligned & _ -2 ² k (4-x² ) d x=1 & 2 ₀² k (4-x² ) d x=1 2 k [4 x- x³ 3 ]_ -0 ²=1 & 2 k (8- 8 3 )=1 2 k ( 16 3 )=1 k= 3 32 & P[-1 < x < 1] & .= _ -1 ¹ ( 3 32 )-4-x² ] d x= 6 32 (4-x² ) d x &= 6 32 4 x- x³ 3 -0 &= 6 32 4- 1 3 = 6 32 11 3 = 11 16 aligned