A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let z be a random variable indicating the number of sessions required to gain the patient's trust. The following probability function has been proposed. S(2) = for a 1,2, or 3 a. Consider the required conditions for a discrete probability function, shown below. f(z) 20 (5.1) Ef(z) = 1 (5.2) Does this probability distribution satisfy equation (5.1)? Yes, all probability function values are greater than or equal to 0 Does this probability distribution satisfy equation (5.2)? Yes, the sum of all probability function values equals 1 b. What is the probability that it takes exactly 2 sessions to gain the patient's trust (to 3 decimals)? 0.5 c. What is the probability that it takes at least 2 sessions to gain the patient's trust (to 3 decimals)?
A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let z be a random variable indicating the number of sessions required to gain the patient's trust. The following probability function has been proposed. S(2) = for a 1,2, or 3 a. Consider the required conditions for a discrete probability function, shown below. f(z) 20 (5.1) Ef(z) = 1 (5.2) Does this probability distribution satisfy equation (5.1)? Yes, all probability function values are greater than or equal to 0 Does this probability distribution satisfy equation (5.2)? Yes, the sum of all probability function values equals 1 b. What is the probability that it takes exactly 2 sessions to gain the patient's trust (to 3 decimals)? 0.5 c. What is the probability that it takes at least 2 sessions to gain the patient's trust (to 3 decimals)?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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Transcribed Image Text:A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let z be a random
variable indicating the number of sessions required to gain the patient's trust. The following probability function has been proposed.
S(2) =
for 1,2, or 3
a. Consider the required conditions for a discrete probability function, shown below.
f(z) 20
(5.1)
Ef(z) = 1
(5.2)
Does this probability distribution satisfy equation (5.1)?
Yes, all probability function values are greater than or equal to 0
Does this probability distribution satisfy equation (5.2)?
Yes, the sum of all probability function values equals 1
b. What is the probability that it takes exactly 2 sessions to gain the patient's trust (to 3 decimals)?
0.5
c. What is the probability that it takes at least 2 sessions to gain the patient's trust (to 3 decimals)?
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