If the p. d. f. of a continuous random variable X is given by f(x) = cases k(9 + 8x - x^2), & for -1 x 4 0, & otherwise cases then the value of k is

Step-by-step solution

Since f(x) is a probability density function, the total probability must be 1 . _ - ^ f(x) dx = 1 _ -1 ⁴ k(9 + 8x - x^2) dx = 1 k [ 9x + 4x^2 - x^3 3 ]_ -1 ⁴ = 1 k ( ( 9(4) + 4(4)^2 - 4^3 3 ) - ( 9(-1) + 4(-1)^2 - (-1)^3 3 ) ) = 1 k ( ( 36 + 64 - 64 3 ) - ( -9 + 4 + 1 3 ) ) = 1 k ( ( 100 - 64 3 ) - ( -5 + 1 3 ) ) = 1 k ( 236 3 - ( - 14 3 ) ) = 1 k ( 250 3 ) = 1 k = 3 250 Answer: 3 250