3: The random variable X takes values 1,2,3 and 4 such that 2P/X=1)= 3P(X=2) = P(X=3)= 5P(X=4). Find K value.
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1
Answer:
Step-by-step explanation:
Given 2P(X=x
1
)=3P(X=x
2
)=P(X=x
3
)=5P(X=x
4
)=k
i=1
∑
4
P(X=x
i
)=1
⟹P(X=x
1
)+P(X=x
2
)+P(X=x
3
)+P(X=x
4
)=1
⟹
2
k
+
3
k
+k+
5
k
=1⟹
30
15k+10k+30k+6k
=1⟹k=
61
30
⟹P(X=x
1
)=
61
15
,P(X=x
2
)=
61
10
,P(X=x
3
)=
61
30
,P(X=x
4
)=
61
6
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