10. Expected value Find the expected value of each random variable: a. b. X P(X=x) X P(X = x) 100 0.1 0 0.2 200 0.2 0.4 300 0.5 2 0.4 400 0.2

Calculate the mean value (expected value) of the following discrete variable x: x-0, 1, 2, 3, 4, 5, 6 %3D p(x) 3D 0.2, 0.2, , 0.05 0.15,0.15, 0.15, 0.1

pls solve bcd Find the expected value of each random variable: a.  x 10 20 30 P(X=x) 0.3 0.5 0.2   b.  x 2 3 4 5 P(X=x) 0.3 0.4 0.2 0.1   c) Find the standard deviation of the random variables in part(a).d) Find the standard deviation of the random variables in part(b

The probability distribution of the random variable X is given in the following table.  Random variable, x  -2 -1 0 1 2 3  P(X = x) 0.10 0.15 0.05 0.20 0.15 0.35   Find the following probabilities. (a)    P(X = 0)(b)    P(X ≤ 0)(c)    P(-1 < X ≤ 4)(d)    P(X ≥ 1)

Directions: Compute the expected value, variance, and standard deviation for random variable X whose probability table is given below: Possible Outcome -1 0 1/7 1/7 Probability Probability Table for X 1. The Expected Value of X is E(X) 2. The Variance of X is Var(X) 3. The Standard Deviation of X is Std(X) 1 2 5/14 5/14

Test for TB TB absent TB present Negative 1739 8 Positive 51 22 Data for TB testing using X-ray imaging Table shows the results of using X-ray imaging as a diagnostic test for tuberculosis in patients with known TB status. Use it to answer the questions below. 1. Calculate the marginal probabilities of the individual random variables, i.e. the probability of positive and negative X-ray test results, and of TB being present and absent. 2. Find the probability of positive result given that TB is absent (false positive rate) and the probability of a negative result given that TB is absent (specificity). 3. Find the probability of negative result given that TB is present (false negative rate) and the probability of a positive result given that TB is present (sensitivity). 4. Find the probability that a person who tests positive actually has TB (probability of TB present given a positive result). 5. Find the probability that a person who tests negative does not have TB (probability of no TB…