What are the mean and standard deviation of the probability density function given by (p(x))/k=x^3-49x for x in [0,7], in terms of k, with k being a constant such that the cumulative density across the range of x is equal to 1?

1 Answer
Jan 27, 2016

Integrate p(x) over [0,7], set equal to 1, then solve for k ...

Explanation:

k=(-4)/2401

Next, using k above, integrate xf(x) over [0,7] to find E(X)

E(X)=56/15

Now, using k above, integrate x^2f(x) over [0,7] to find E(X^2)

E(X^2)=49/3

Find the Variance:

sigma^2=E(X^2)=[E(X)]^2=49/3-(56/15)^2=539/225

Finally, standard deviation sigma=sqrt(sigma^2)=(7sqrt11)/15

If you really need to know the mean and standard deviation in terms of k , then simply divide these parameters by k=(-4)/2401, then multiply each by the variable k.

hope that helped!

Note: Used the Solver feature of my TI-84 to find all these values:)