For the following probability mass function, p(x)=1/x for x=2, 4, 8 p(x) = k/x2 for x=16...

For the following probability mass function, p(x)=1/x for x=2, 4, 8 p(x) = k/x2 for x=16 Find the value of k. Find the standard deviation of (7-9X).

Solutions

Expert Solution

1) for this to be valid:

P(x) must be equal to 1

therefore P(x) =P(2)+P(4)+P(8)+P(16)=(1/2)+(1/4)+(1/8)+k/256 =1

k/256 =1/8

k=32

x	P(x)	xP(x)	x²P(x)
2	1/2	1.0000	2.0000
4	1/4	1.0000	4.0000
8	1/8	1.0000	8.0000
16	1/8	2.0000	32.0000
	total	5.0000	46.0000

	E(x) =μ=	ΣxP(x) =	5.0000
	E(x²) =	Σx²P(x) =	46.0000
	Var(x)=σ² =	E(x²)-(E(x))²=	21.0000
	std deviation=	σ= √σ² =	4.5826

hence standard deviation of 7-9X =9*SD(X) =9*4.5826 =41.2432

orchestra answered 1 year ago

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