Standard Deviation about Mean for Continuous Frequency Distributions
A random vari...
Question
A random variable X has the following p.d.f.
X
0
1
2
3
4
5
6
7
P(X=x)
0
k
2k
2k
3k
k2
2k2
7k2+k
The value of k is
A
18
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B
110
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C
0
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D
−1
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Solution
The correct option is B110 x=7∑x=0P(X)=1 ⇒P(0)+P(1)+P(2)...P(7)=1 ⇒0+k+2k+2k+3k+k2+2k2+7k2+k=1 ⇒10k2+9k−1=0 ⇒10k2+10k−k−1=0 ⇒10k(k+1)−(k+1)=0 ⇒(k+1)(10k−1)=0 k=−1 or k=110.