Suppose that A, B, C, are independent random variables, each being uniformly distributed over (0, 1). (a) What is the joint cumu
lative distribution function of A, B, C? (b) What is the probability that all of the roots of the equation Ax2 + Bx + C = 0 are real?
1 answer:
Answer:
a) F (A , B,C)(a,b,c) = abc
b) Answer is in derivative
Step-by-step explanation:
Hence area is maximum x=6
For ( a,b,c) ∈ (0,1)
We have that
F A, B,C (a,b,c) = A≤ a , B≤ b , C≤c
=P (A≤a) P (B≤b) P (C≤c)
A , B, C ≈ unit (0,1) we have that
P (A≤a) =a
P (B≤b) =b
P (C≤c)=c
Thus
F (A , B,C)(a,b,c) = abc
b) Answer is in derivative
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The probability that no one in the family of 4 will be hospitalized during a year is 0.52
Step-by-step explanation:
The probability for a person to be hospitalized during one year is
As a consequence, the probability for a person of NOT being hospitalized during one year is
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So, the probability that no one in the family of 4 will be hospitalized during a year is 0.52.
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