Find the value of λ such that the function f(x) is a valid probability density function. f(x)=λ(x−1)(2−x) for 1≤x≤2 =0 otherwise
A function f(x) is designed as to be a valid probability density function the value of A must be f(x)=⎧⎪ ⎪ ⎪⎨⎪ ⎪ ⎪⎩0;x<31A(3x+5) ;3<x<6. Forf(x)0;x>6
The probability density function of a random variable X is Px(x)=e−x for x≥0 and 0 otherwise. The expected value of the function gx(x)=e3x/4 is .