Question 32 - Week 4 Practice | Prasnya
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Week 4
Question 32
00:00
Est. 2 min
Marks:
+2.00
0.00
Let
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
be defined by
f
(
x
)
=
{
0
,
−
∞
<
x
<
0
,
1
4
,
0
<
x
≤
1
,
3
4
x
2
,
1
<
x
<
∞
.
f(x)=\begin{cases}0, & -\infty < x < 0,\\ \frac{1}{4}, & 0 < x \le 1,\\ \frac{3}{4x^2}, & 1 < x < \infty.\end{cases}
If a random variable
X
X
has the PDF
f
(
x
)
f(x)
, calculate
P
(
−
1
2
<
X
<
3
2
)
P\left(-\frac{1}{2}<X<\frac{3}{2}\right)
. Enter the answer correct to one decimal place. Hint: use
∫
a
b
1
x
2
d
x
=
1
a
−
1
b
\int_a^b \frac{1}{x^2}\,dx = \frac{1}{a}-\frac{1}{b}
.
Integer answer
Medium Difficulty
05 June 2022
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