Question 1 - Week 4 Practice | Prasnya
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Week 4
Question 1
00:00
Est. 2 min
Marks:
+3.00
0.00
Let
X
X
be a continuous random variable with the following CDF:
F
X
(
x
)
=
{
0
,
x
<
−
1
(
x
+
1
)
2
2
,
−
1
≤
x
<
0
1
−
(
1
−
x
)
2
2
,
0
≤
x
<
1
1
,
x
≥
1
F_X(x)=\begin{cases}0, & x<-1\\\frac{(x+1)^2}{2}, & -1\le x<0\\1-\frac{(1-x)^2}{2}, & 0\le x<1\\1, & x\ge 1\end{cases}
Which of the following is the correct PDF of
X
X
?
Single correct
Medium Difficulty
26 October 2025
A
f
X
(
x
)
=
{
1
−
x
,
−
1
≤
x
<
0
1
+
x
,
0
≤
x
<
1
0
,
otherwise
f_X(x)=\begin{cases}1-x, & -1\le x<0\\1+x, & 0\le x<1\\0, & \text{otherwise}\end{cases}
B
f
X
(
x
)
=
{
x
+
1
,
−
1
≤
x
<
1
0
,
otherwise
f_X(x)=\begin{cases}x+1, & -1\le x<1\\0, & \text{otherwise}\end{cases}
C
f
X
(
x
)
=
{
x
,
−
1
≤
x
<
1
0
,
otherwise
f_X(x)=\begin{cases}x, & -1\le x<1\\0, & \text{otherwise}\end{cases}
D
f
X
(
x
)
=
{
x
+
1
,
−
1
≤
x
<
0
1
−
x
,
0
≤
x
<
1
0
,
otherwise
f_X(x)=\begin{cases}x+1, & -1\le x<0\\1-x, & 0\le x<1\\0, & \text{otherwise}\end{cases}
