Question

# Each time a hurricane arrives, a new home has a 0.4 probability of experiencing damage. The...

Each time a hurricane arrives, a new home has a 0.4 probability of experiencing damage. The occurrences of damage in different hurricanes are mutually independent.

Q3 a) What is the probability that the fourth house damaged on eighth hurricane? (Round your answer to 4 decimal places.) *

6 points

Q3 b) What is the expected value that the fourth house damaged on eighth hurricane? *

6 points

Q3 c) What is the variance that sixth house damaged on tenth hurricane?

Let r be the number of houses damaged.

x be the number of hurricanes required to damage r houses.

p is probability of experiencing damage.

x follows negative binomial distribution.

P( x ) = , x = 0,1,2...

a) Given : r = 4 , x = 8 and p = 0.4

P ( x = 8 ) =

=

= 35*0.0256*0.1296

= 0.1161

b) r = 4 ,x = 8 , p = 0.4

Expected value = r / p = 4/0.4

Expected value = 10

c) r = 6 , x = 10 and p = 0.4

Variance = =

Variance = 22.5

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