Find $\mathrm{k}$ such that the function is a probability density function over the given interval. Then write the probability density function.
\[
f(x)=k x^{2},[-4,5]
\]
$k=\square$ (Type an exact answer.)
The probability density function is $f(x)=\square$. (Type an exact answer.)
Answer
Final Answer: The value of k is \(\boxed{\frac{1}{63}}\). The probability density function is \(f(x)=\boxed{\frac{x^{2}}{63}}\).
Step 1 ：The integral of a probability density function over its entire domain must be equal to 1. Therefore, we need to find the value of k such that the integral of kx^2 from -4 to 5 is equal to 1.
Step 2 ：Calculate the integral of kx^2 from -4 to 5, which equals to 63*k.
Step 3 ：Set the integral equal to 1, we get k = 1/63.
Step 4 ：Final Answer: The value of k is \(\boxed{\frac{1}{63}}\). The probability density function is \(f(x)=\boxed{\frac{x^{2}}{63}}\).
