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Let X be a continuous random variable with a probability density function f(x) …
Related Topics
Wize University Calculus 2 Textbook > Applications of Integrals
Probability
6 Activities
Let
X
X
X
be a continuous random variable with a probability density function
f
(
x
)
=
{
c
e
−
4
x
,
0
≤
x
0
,
otherwise
f(x) = \left \{ \begin{array}{ll} ce^{-4x}, & 0 \leq x \\ 0, & \text{otherwise} \end{array} \right .
f
(
x
)
=
{
c
e
−
4
x
,
0
,
0
≤
x
otherwise
First, determine the value of
c
c
c
that makes the function a PDF. Then determine
P
(
9
≤
X
≤
11
)
P(9 \leq X \leq 11)
P
(
9
≤
X
≤
11
)
.
Value of c
P
(
9
≤
X
≤
11
)
P(9 \leq X \leq 11)
P
(
9
≤
X
≤
11
)
I don't know
Check Submission
More Probability Questions:
The probability density function for the number of times a child screams during a roller coaster is given by
f
(
x
)
=
{
1
6
π
(
1
−
cos
(
2
x
)
)
,
0
≤
x
≤
6
π
0
,
otherwise
f(x) = \left \{ \begin{array}{ll} \displaystyle \frac{1}{6 \pi}(1 - \cos(2x)), & 0\leq x \leq 6 \pi \\\\ 0, & \text{otherwise} \end{array} \right .
f
(
x
)
=
⎩
⎨
⎧
6
π
1
(
1
−
cos
(
2
x
))
,
0
,
0
≤
x
≤
6
π
otherwise
Find the mean number of screams over the course of the ride.
Let
X
X
X
be a random variable with values that range within
[
0
,
2
]
[0, 2]
[
0
,
2
]
with pdf
p
(
x
)
=
3
8
x
2
p(x) = \frac{3}{8}x^2
p
(
x
)
=
8
3
x
2
Compute the mean, and standard deviation of this distribution.