+0

# IB Stats

0
146
1

Idk how to even do this kinda problem

Feb 8, 2021

#1
+8457
+1

Definition of a probability density function:

If f(x) is a probability density function, then $$\displaystyle \int^6_0 f(x)\,dx = 1$$.

This means for the probability density function in the question, $$\displaystyle \int^6_0 Ax(6 - x)\,dx = 1$$.

Now, notice that $$\displaystyle \int^6_0 x(6- x)\,dx = 36$$.

Therefore A = 1/36.

For part B, sketching a quadratic function should be easy.

For part C, just find $$\displaystyle \int^6_4 f(x)\,dx$$.

For part D, let W be the weight of a random jar. We can find $$\mathbb E(W) = \displaystyle \int^6_0 xf(x)\,dx$$ and $$\mathbb E(W^2) = \displaystyle \int^6_0 x^2f(x)\,dx$$ and then use the formula $$\operatorname{Var}(W) = \mathbb E(W^2) - \left(E(W)\right)^2$$

You should know how the standard deviation and the variance are related.

Feb 8, 2021