Question

Consider the following probability distribution.

xi	P(X = xi)
–2	0.2
–1	0.1
0	0.3
1	0.4

The variance is _____.

The expected value is _____.

The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States, but even when analysis is restricted to relatively strong housing markets the numbers are staggering. For example, in 2017 an average of three residential properties were auctioned off each weekday in the city of Boston, up from an average of one per week in 2011. What is the probability that at least one foreclosure auction occurred in Boston on a randomly selected weekday of 2017?

Answer 1

x	P(x)	xP(x)	x2P(x)
-2	0.200	-0.400	0.800
-1	0.100	-0.100	0.100
0	0.300	0.000	0.000
1	0.400	0.400	0.400
	total	-0.100	1.300
	E(x) =μ=	ΣxP(x) =	-0.1000
	E(x2) =	Σx2P(x) =	1.3000
	Var(x)=σ2 =	E(x2)-(E(x))2=	1.2900

The variance is =1.29

The expected value is =-0.10

2)

from poisson distribution:

probability that at least one foreclosure auction occurred in Boston on a randomly selected weekday of 2017 =1-P(none occurs)=1-e^-3*3⁰/0! =0.950213