Suppose that the probability density function of the amount of milk deposited in a milk container is: f(X)=40.976-16x^2-30e^(-x) for 1.95<=x<=2.1

Mylo O'Moore

Mylo O'Moore

Answered question

2021-09-16

Suppose that the probability density function of the amount of milk deposited in a milk container is:
f(X)=40.97616x230ex for 1.95x2.1 Liters.
a) Calculate the probability that the actual amount of milk deposited is less than 2 liters.
b) Calculate the Expected Value in Liters of this distribution.

Answer & Explanation

sweererlirumeX

sweererlirumeX

Skilled2021-09-17Added 91 answers

a) Total prbability distribution value = 1
for 1.95x2.1
Probability value: 1.952.1f(x)dx
=1.952(40.97616x230ex)dx
=|40.976x16x2230ex(1)|1.952
=(40.976216222+30e2)(40.9761.95161.9522+30e1.95)
=0.4681=46.81%
b) Expected value =1.952.1xf(x)dx
=1.952.1x(40.97616x630ex)dx
=|40.976x2216x3330(xexex)|1.952.1
=1.39liters

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