Let X be a random variable of the mixed type having the

Chapter 3, Problem 7E

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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)

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


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