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Patients given drug therapy either improve, remain the
Chapter 5, Problem 56E(choose chapter or problem)
Patients given drug therapy either improve, remain the same, or degrade with probabilities 0.5, 0.4, 0.1, respectively. Suppose that 20 patients (assumed to be independent) are given the therapy. Let \(X_{1}, X_{2}\), and \(X_{3}\) denote the number of patient who improved, stayed the same, or became degraded. Determine the following.
(a) Are \(X_{1}, X_{2}, X_{3}\) independent? (b) \(P\left(X_{1}=10\right)\)
(c) \(P\left(X_{1}=10, X_{2}=8, X_{3}=2\right)\) (d) \(P\left(X_{1}=5 \mid X_{2}=12\right)\)
(e) \(E\left(X_{1}\right)\)
Equation transcription:
Text transcription:
X{1}, X{2}
X{3}
X{1}, X{2}, X{3}
P(X{1}=10)
P(X{1}=10, X{2}=8, X{3}=2)
P(X{1}=5 mid X{2}=12)
E(X{1})
Questions & Answers
QUESTION:
Patients given drug therapy either improve, remain the same, or degrade with probabilities 0.5, 0.4, 0.1, respectively. Suppose that 20 patients (assumed to be independent) are given the therapy. Let \(X_{1}, X_{2}\), and \(X_{3}\) denote the number of patient who improved, stayed the same, or became degraded. Determine the following.
(a) Are \(X_{1}, X_{2}, X_{3}\) independent? (b) \(P\left(X_{1}=10\right)\)
(c) \(P\left(X_{1}=10, X_{2}=8, X_{3}=2\right)\) (d) \(P\left(X_{1}=5 \mid X_{2}=12\right)\)
(e) \(E\left(X_{1}\right)\)
Equation transcription:
Text transcription:
X{1}, X{2}
X{3}
X{1}, X{2}, X{3}
P(X{1}=10)
P(X{1}=10, X{2}=8, X{3}=2)
P(X{1}=5 mid X{2}=12)
E(X{1})
ANSWER:Solution 56E
Step1 of 6:
Let us considera a random variables presents:
The number of improved patients.
The number of patients with same health.
The number of patients with degraded health.
Here our goal is:
a). We need to check ,
, and
are independent or not.
b). We need to find
c). We need to find
d). We need to find
e). We need to find
Step2 of 6:
a).
Let all three random variables follows binomial distribution with:
Here the health of the patients are independent of others and so the number of patients with respect to their health condition is also independent. Hence, ,
, and
are independent.
Step3 of 6:
b).
Consider,