solution
i) PDF of X
For a uniform distribution,
f(x)=b−a1 For X between 5 and 15 ounces:
f(x)=15−51=101
Answer: f(x)=101
ii) Probability that 12<X<15
f(12<X<15)=(15−12)∗101=103
answer: f(12<x<15)=103
iii) probability that X<5
The domain of X is the range of values where the PDF is valid. The domain of X=[5,15]
The PDF is not valid for values of X<5
answer: f(X<5)=0
iv) E(X) and Var(X)
E(X)=2b+a
=215+5=10
Var(X)=12(b−a)2
=12(15−5)2=12100=8.3333
answer: E(X)=10 and Var(X)=8.3333
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