x 0 1 2 3 4 P(X) 0.45 0.3 0.2 0.04 0.01 (a) Find and interpret...

x	0	1	2	3	4
P(X)	0.45	0.3	0.2	0.04	0.01

(a) Find and interpret the expected value of X

(b)Find the variance of X

(c)Find the probability that a person has 1 sibling given that they have less than 3 siblings.

(d)Find the probability that a person has at least 1 sibling OR less than 2 siblings

Solutions

Expert Solution

Solution

x	P(x)	*x P(x)**	*x² P(x)**
0	0.45	0	0
1	0.3	0.3	0.3
2	0.2	0.4	0.8
3	0.04	0.12	0.36
4	0.01	0.04	0.16
	1	0.86	1.62

a ) Mean = = X * P(X) = 0.86

b ) variance = ² =X ² * P(X) - ²

² =1.62 - 0.7396

²=0.8804

² = 0.93

c ) P ( x < 3 )

= P ( x = 0 ) + P ( x = 1 ) + P ( x = 2 )

= 0.45 +0.3 +0.2

= 0.95

probability= 0.95

d ) P ( x 2 )

= P ( x = 2 ) + P ( x = 3 ) + P ( x = 4)

= 0.2 +0.04 +0.01

= 0.25

probability= 0.25

orchestra answered 1 year ago

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