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Byju's Answer
Standard XII
Mathematics
Binomial Probability Theorem
For what valu...
Question
For what value of k the following distribution is a probability distribution?
X = x
i
:
0
1
2
3
P (X = x
i
) :
2k
4
3k
2
− 5k
3
2k − 3k
2
3k − 1
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Solution
We know that the sum of probabilities in a probability distribution is always 1.
∴ P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) = 1
⇒
2
k
4
+
3
k
2
-
5
k
3
+
2
k
-
3
k
2
+
3
k
-
1
=
1
⇒
2
k
4
-
5
k
3
+
5
k
=
2
⇒
2
k
4
-
5
k
3
+
5
k
-
2
=
0
⇒
k
-
1
k
-
2
2
k
2
+
k
-
1
=
0
⇒
k
-
1
k
-
2
2
k
-
1
k
+
1
=
0
⇒
k
=
-
1
,
1
2
,
1
,
2
Neglecting
-
1
,
1
and
2
as
they
give
the
value
of
probability
negative
or
greater
than
1
∴ k =
1
2
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