The snowfall in inches at a particular location is given by the following probability density function: f(x): f(x) f(x) = 2x 125 2 25 20 125 125 0≤x≤5 5 ≤ x ≤ 10 10 ≤ x ≤20 a) Verify that the above function satisfies the property of a PDF. b) A severe snowstorm is defined as a snow storm whose snowfall is greater than or equal to 12 inches. A snowstorm is termed as disastrous if the snowfall is greater than or equal to 16 inches. If we know a particular snowstorm is severe, what is the probability that the snowstorm will be disastrous? c) In a year, the location experiences three snowstorms. What is the probability that at least one of the three snow storms is severe (assume the amount of snow falling in each snow storm is independent)?

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The snowfall in inches at a particular location is given by the following probability density
function:
f(x):
=
f(x)
f(x)=
2x
125
25
20
I
125 125
0 ≤x≤5
5 ≤ x ≤ 10
10 ≤ x ≤ 20
a) Verify that the above function satisfies the property of a PDF.
b) A severe snowstorm is defined as a snow storm whose snowfall is greater than or equal
to 12 inches. A snowstorm is termed as disastrous if the snowfall is greater than or
equal to 16 inches. If we know a particular snowstorm is severe, what is the probability
that the snowstorm will be disastrous?
c) In a year, the location experiences three snowstorms. What is the probability that at
least one of the three snow storms is severe (assume the amount of snow falling in each
snow storm is independent)?
Transcribed Image Text:The snowfall in inches at a particular location is given by the following probability density function: f(x): = f(x) f(x)= 2x 125 25 20 I 125 125 0 ≤x≤5 5 ≤ x ≤ 10 10 ≤ x ≤ 20 a) Verify that the above function satisfies the property of a PDF. b) A severe snowstorm is defined as a snow storm whose snowfall is greater than or equal to 12 inches. A snowstorm is termed as disastrous if the snowfall is greater than or equal to 16 inches. If we know a particular snowstorm is severe, what is the probability that the snowstorm will be disastrous? c) In a year, the location experiences three snowstorms. What is the probability that at least one of the three snow storms is severe (assume the amount of snow falling in each snow storm is independent)?
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