Question

Suppose the X is a continuous random variable whose probability density function is given by \begin{cases} kx, & 0 \le x < 3, \ 2 - \frac{x}{2}, & 3 \le x \le 4, \ 0, & \text{otherwise} \end{cases} (a) What is the value of k? (b) What is the cumulative distribution function of X, F(x)? (c) Find P \{1 < X \le \frac{7}{2}\}

          Suppose the X is a continuous random variable whose probability density
function is given by
\begin{cases}
kx, & 0 \le x < 3, \
2 - \frac{x}{2}, & 3 \le x \le 4, \
0, & \text{otherwise}
\end{cases}
(a) What is the value of k?
(b) What is the cumulative distribution function of X, F(x)?
(c) Find P \{1 < X \le \frac{7}{2}\}

Suppose the X is a continuous random variable whose probability density
function is given by

kx, 0 ≤x < 3, 2 - (x)/(2), 3 ≤x ≤4, 0, otherwise

(a) What is the value of k?
(b) What is the cumulative distribution function of X, F(x)?
(c) Find P {1 < X ≤(7)/(2)}

Added by Deanna G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Hoan Nguyen

12/06/2023

Step 1

Step 1: For a probability density function, the integral over the entire domain must equal 1. Show more…

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Suppose the X is a continuous random variable whose probability density function is given by $$ f(x) = \begin{cases} kx, & 0 \le x < 3, \\ 2 - \frac{x}{2}, & 3 \le x \le 4, \\ 0, & \text{otherwise} \end{cases} $$ (a) What is the value of k? (b) What is the cumulative distribution function of X, F(x)? (c) Find P {1 < X ≤ 2}