Find $k$ such that the function is a probability density function over the given interval. Then write the probability density function.
$f (x) = k x^{2}, [- 4, 5]$
$k = ◻$ (Type an exact answer.)
The probability density function is $f (x) = ◻$ . (Type an exact answer.)

Answer

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Final Answer: The value of k is $\frac{1}{63}$ . The probability density function is $f (x) = \frac{x^{2}}{63}$ .

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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 $\frac{1}{63}$ . The probability density function is $f (x) = \frac{x^{2}}{63}$ .

Find k such that the function is a probability density function over the given interval. Then write the probability density function.f(x)=kx2,[−4,5]k=◻ (Type an exact answer.)The probability density function is f(x)=◻. (Type an exact answer.)

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Find $k$ such that the function is a probability density function over the given interval. Then write the probability density function.
$f (x) = k x^{2}, [- 4, 5]$
$k = ◻$ (Type an exact answer.)
The probability density function is $f (x) = ◻$ . (Type an exact answer.)