Question 23 - Week 4 Practice | Prasnya
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Week 4
Question 23
00:00
Est. 3 min
Marks:
+3.00
0.00
Consider a function
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
such that
f
(
x
)
=
c
x
2
f(x)=cx^2
for
1
≤
x
<
2
1\le x<2
,
f
(
x
)
=
c
x
f(x)=cx
for
2
≤
x
<
4
2\le x<4
, and
f
(
x
)
=
0
f(x)=0
otherwise, where
c
c
is any real constant. Find
c
c
such that
f
f
is a valid density function. Enter the answer correct to two decimal places. Hint:
∫
x
k
d
x
=
x
k
+
1
k
+
1
\int x^k\,dx=\frac{x^{k+1}}{k+1}
.
Integer answer
Medium Difficulty
29 October 2023
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