Solution Found!
Let X be a random variable of the mixed type having the
Chapter 3, Problem 7E(choose chapter or problem)
Let \(X\) be a random variable of the mixed type having the cdf
\(F(x)= \begin{cases}0, & x<0, \\ \frac{x^{2}}{4}, & 0 \leq x<1, \\ \frac{x+1}{4}, & 1 \leq x<2, \\ 1, & 2 \leq x .\end{cases}\)
(a) Carefully sketch the graph of \(F(x)\).
(b) Find the mean and the variance of \(X\).
(c) Find \(P(1 / 4<X<1), P(X=1), P(X=1 / 2)\), and \(P(1 / 2 \leq X<2)\).
Equation Transcription:
{
Text Transcription:
X
F(x)= {1, 2 < or =x. x+1/4, 1 < or = x<2. x^2/4, 0 < or = x<1, 0, x< 0,
F(x)
P(1/4 < X < 1), P(X = 1), P(X = 1/2)
P(1/2 < or = X < 2)
Questions & Answers
QUESTION:
Let \(X\) be a random variable of the mixed type having the cdf
\(F(x)= \begin{cases}0, & x<0, \\ \frac{x^{2}}{4}, & 0 \leq x<1, \\ \frac{x+1}{4}, & 1 \leq x<2, \\ 1, & 2 \leq x .\end{cases}\)
(a) Carefully sketch the graph of \(F(x)\).
(b) Find the mean and the variance of \(X\).
(c) Find \(P(1 / 4<X<1), P(X=1), P(X=1 / 2)\), and \(P(1 / 2 \leq X<2)\).
Equation Transcription:
{
Text Transcription:
X
F(x)= {1, 2 < or =x. x+1/4, 1 < or = x<2. x^2/4, 0 < or = x<1, 0, x< 0,
F(x)
P(1/4 < X < 1), P(X = 1), P(X = 1/2)
P(1/2 < or = X < 2)
ANSWER:
Answer
Step 1 of 5
For sketching the graph
Take x values on the X-axis
And F(x) values on the Y-axis