Question

The pdf of a random variable is given as egin{equation} f_X(x) = egin{cases} kx, & 0 le x le 1\ 0, & ext{otherwise} end{cases} end{equation} 1) Find the constant $k$. 2) Find the CDF $F_X(x)$ 3) Find $P(A)$ where $A = {0 < X < 0.5}$ 4) Find $f_{X|A}(x)$

          The pdf of a random variable is given as
egin{equation*}
f_X(x) = egin{cases} kx, & 0 le x le 1\ 0, & 	ext{otherwise} end{cases}
end{equation*}
1) Find the constant $k$.
2) Find the CDF $F_X(x)$
3) Find $P(A)$ where $A = {0 < X < 0.5}$
4) Find $f_{X|A}(x)$

The pdf of a random variable is given as
eginequation*
fX(x) = egincases kx, 0 le x le 1 0, extotherwise endcases
endequation*
1) Find the constant k.
2) Find the CDF FX(x)
3) Find P(A) where A = 0 < X < 0.5
4) Find fX|A(x)

Added by Amanda M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Danielle Fairburn

11/27/2023

Step 1

We can do this by integrating the pdf over the given range and setting it equal to 1: $$ \int_0^1 kx \, dx = 1 $$ Now, we can solve for k: $$ k \int_0^1 x \, dx = 1 \\ k \left[\frac{1}{2}x^2\right]_0^1 = 1 \\ k \cdot \frac{1}{2} = 1 \\ k = 2 $$ So, the pdf Show more…

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The pdf of a random variable is given as: f_X(x) = { kx, 0 <= x <= 1 0, otherwise } 1) Find the constant k. 2) Find the CDF F_X(x). 3) Find P(A) where A = {0 < X < 0.5}. 4) Find f_{X|A}(x).