### Understanding Probability Distribution for Patient TrustA psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let $ x $ be a random variable indicating the number of sessions required to gain the patient’s trust. The following probability function has been proposed:\[ f(x) = \frac{x}{6} \quad \text{for } x = 1, 2, \text{ or } 3 \]#### a. Conditions for a Discrete Probability FunctionConsider the required conditions for a discrete probability function, shown below:1. $ f(x) \geq 0 $ *Equation (5.1)* 2. $\sum f(x) = 1 $ *Equation (5.2)*- **Does this probability distribution satisfy equation (5.1)?** [Dropdown option: Yes/No]- **Does this probability distribution satisfy equation (5.2)?** [Dropdown option: Yes/No]#### b. Probability for Exactly 2 SessionsWhat is the probability that it takes exactly 2 sessions to gain the patient’s trust (to 3 decimals)?\[ \text{Probability} (x=2) = \frac{2}{6} = 0.333 \]#### c. Probability for At Least 2 SessionsWhat is the probability that it takes at least 2 sessions to gain the patient’s trust (to 3 decimals)?\[ \text{Probability} (x \geq 2) = f(2) + f(3) = \frac{2}{6} + \frac{3}{6} = 0.333 + 0.500 = 0.833 \]This framework allows students and educators to assess how well a proposed probability function meets theoretical criteria and calculate specific probabilities for decision-making.

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Description: ### Understanding Probability Distribution for Patient TrustA psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let $ x $ be a random variable indicating the number of sessions

Given: fX(x)=x6 , x = 1, 2, 3 Part a: We have fX(1)=16>0 , x=1 fX(2)=26>0 , x=2 fX(3)=36>0 , x=3 Therefore, for x = 1, 2, 3 condition (5.1) is satisfied. Also ∑xfX(x) = fX(1)+ fX(2)+ fX(3) = 16+26+36=1 Therefore, for x = 1, 2, 3 condition (5.2) is satisfied. Part b: The required probability is P(X=2) =fX(2) =26 =0.333 Part c: The required probability is P(X≥2) =fX(2) +fX(3)=26 +36=0.833

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A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3 Let be a random variable indicating the number of sessions required to gain the patient's trust. The following probability function has been proposed. f(x) = for a = 1, 2, or 3 a. Consider the required conditions for a discrete probability function, shown below. f(æ) > 0 (5.1) Ef(#) = 1 (5.2) Does this probability distribution satisfy equation (5.1)? - Select your answer - Does this probability distribution satisfy equation (5.2)? - Select your answer- b. What is the probability that it takes exactly 2 sessions to gain the patient's trust (to 3 decimals)? 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 be a random variable indicating the number of sessions required to gain the patient's trust. The following probability function has been proposed. f(x) = for a = 1, 2, or 3 a. Consider the required conditions for a discrete probability function, shown below. f(æ) > 0 (5.1) Ef(#) = 1 (5.2) Does this probability distribution satisfy equation (5.1)? - Select your answer - Does this probability distribution satisfy equation (5.2)? - Select your answer- b. What is the probability that it takes exactly 2 sessions to gain the patient's trust (to 3 decimals)? 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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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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### Understanding Probability Distribution for Patient Trust

A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let $ x $ be a random variable indicating the number of sessions required to gain the patient’s trust. The following probability function has been proposed:

\[ f(x) = \frac{x}{6} \quad \text{for } x = 1, 2, \text{ or } 3 \]

#### a. Conditions for a Discrete Probability Function

Consider the required conditions for a discrete probability function, shown below:

1. $ f(x) \geq 0 $
*Equation (5.1)*

2. $\sum f(x) = 1 $
*Equation (5.2)*

- **Does this probability distribution satisfy equation (5.1)?**
[Dropdown option: Yes/No]

- **Does this probability distribution satisfy equation (5.2)?**
[Dropdown option: Yes/No]

#### b. Probability for Exactly 2 Sessions

What is the probability that it takes exactly 2 sessions to gain the patient’s trust (to 3 decimals)?

\[ \text{Probability} (x=2) = \frac{2}{6} = 0.333 \]

#### c. Probability for At Least 2 Sessions

What is the probability that it takes at least 2 sessions to gain the patient’s trust (to 3 decimals)?

\[ \text{Probability} (x \geq 2) = f(2) + f(3) = \frac{2}{6} + \frac{3}{6} = 0.333 + 0.500 = 0.833 \]

This framework allows students and educators to assess how well a proposed probability function meets theoretical criteria and calculate specific probabilities for decision-making.

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