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) = 2060 x for x = 1, 2, or 3 a. Consider the required conditions for a discrete probability function, shown below. f(x) 0 f(x)=1 (5.1) (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)? c. What is the probability that it takes at least 2 sessions to gain the patient's trust (to 3 decimals)? The following table provides a probability distribution for the random variable . Excel File: data05-15.xlsx 2360 f(x) 0.25 0.50 9 0.25 a. Compute E(a), the expected value of . b. Compute 2, the variance of a (to 1 decimal). c. Compute , the standard deviation of (to 2 decimals).