Question 19 - Week 4 Practice | Prasnya
Prasnya
Continue with Google
Practice path
Dashboard
Exam
Qualifier / Quiz 1
Go to subject
Statistics 2
Go to chapter
Week 4
Question 19
00:00
Est. 2 min
Marks:
+3.00
0.00
Passage
Based on the above data, answer the given subquestions. Let
X
X
be a continuous random variable with the following PDF:
f
X
(
x
)
=
{
c
x
2
(
1
−
x
)
,
0
≤
x
≤
1
,
0
,
otherwise
.
f_X(x)=\begin{cases}cx^2(1-x), & 0\le x\le1,\\ 0, & \text{otherwise}.\end{cases}
Question
Calculate the CDF of
X
X
.
Comprehension
Medium Difficulty
07 July 2024
A
F
X
(
x
)
=
0
F_X(x)=0
for
x
<
0
x<0
;
4
x
3
−
3
x
4
4x^3-3x^4
for
0
≤
x
<
1
0\le x<1
;
1
1
for
x
≥
1
x\ge1
B
F
X
(
x
)
=
0
F_X(x)=0
for
x
<
0
x<0
;
1
12
(
x
3
3
−
x
4
4
)
\frac{1}{12}\left(\frac{x^3}{3}-\frac{x^4}{4}\right)
for
0
≤
x
<
1
0\le x<1
;
1
1
for
x
≥
1
x\ge1
C
F
X
(
x
)
=
0
F_X(x)=0
for
x
<
0
x<0
;
24
x
−
36
x
2
24x-36x^2
for
0
≤
x
<
1
0\le x<1
;
1
1
for
x
≥
1
x\ge1
D
F
X
(
x
)
=
0
F_X(x)=0
for
x
<
0
x<0
;
x
6
−
x
2
4
\frac{x}{6}-\frac{x^2}{4}
for
0
≤
x
<
1
0\le x<1
;
1
1
for
x
≥
1
x\ge1
