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Byju's Answer
Standard XII
Mathematics
Probability Distribution
A random vari...
Question
A random variable
x
has the following probability distribution:
x
0
1
2
3
4
5
6
P
(
X
=
x
)
k
3
k
5
k
7
k
9
k
11
k
13
k
Find
′
k
′
.
Open in App
Solution
x
0
1
2
3
4
5
6
P
(
X
=
x
)
k
3
k
5
k
7
k
9
k
11
k
13
k
We know,
6
∑
r
=
0
P
(
X
=
x
)
=
1
∴
k
+
3
k
+
5
k
+
7
k
+
9
k
+
11
k
+
13
k
=
1
49
k
=
1
k
=
1
49
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0
Similar questions
Q.
A random variable
X
has the following probability distribution:
X
=
x
0
1
2
3
4
5
6
P
(
X
=
x
)
k
3
k
5
k
7
k
9
k
11
k
13
k
(a) Find
k
(b) Find
P
(
0
<
X
<
4
)
(c) Obtain cumulative distribution function (c.d.f) of
X
.
Q.
A random variable
X
has the following probability mass function.
x
0
1
2
3
4
5
6
P
(
X
=
x
)
k
3
k
5
k
7
k
9
k
11
k
13
k
(a) Find
k
.
(b) Evaluate
P
(
X
<
4
)
,
P
(
X
≥
5
)
and
P
(
3
<
X
≤
6
)
.
(c) What is the smallest value of
x
for which
P
(
X
≤
x
)
>
1
2
?
Q.
A random variable X has following probability distribution.
X
=
x
1
2
3
4
5
6
P
(
X
=
x
)
K
3
K
5
K
7
K
8
K
K
Then
P
(
2
≤
x
<
5
)
=
_______.
Q.
A random variable
X
has the following probability distribution:
X
0
1
2
3
4
5
6
7
P
(
X
)
0
k
2
k
2
k
3
k
k
2
2
k
2
7
k
2
+
k
Determine
(i)
k
(ii)
P
(
X
<
3
)
(iii)
P
(
X
>
6
)
(iv)
P
(
0
<
X
<
3
)
Q.
A random variable
X
has the following probability distribution.
X
=
x
0
1
2
3
4
5
6
7
P
(
X
=
x
)
0
k
2
k
2
k
3
k
k
2
2
k
2
7
k
2
+
k
Find (i)
k
(ii) The mean and (iii)
P
(
0
<
X
<
5
)
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