(c) Assume the following respective probabilities for the posi- tions of the two loads: P(W, at B) = 0.25 %3D P(W, at C) = 0.60 P(W2 at B) = 0.30 P(W2 at C) = 0.50 Assuming that the positions of W, and W, are statistically in- dependent; what are the respective probabilities associated with each of the possible values of MA? (d) Determine the probabilities of the following events: E1, E2, E3. E, N E2, E, U E2, and E2

Q.1 Let X is the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has probability mass function 13.5 15.9 19.1 P(X = x) 0.2 0.5 0.3 (1) If the price of a freezer having capacity X cubic feet 8.5, what is the expected price and variance paid is 25X by the next cust omer to buy a freezer? (ii) Find moment generating function.

Consider a binary response variable y and a predictor variable x. The following table contains the parameter estimates of the linear probability model (LPM) and the logistic regression model, with the associated p-values shown in parentheses. Variable Intercept x LPM Logistic -6.90 (0.06) 0.19 (0.06) a. Test for the significance of the intercept and the slope coefficients at the 5% level in both models. Coefficients Intercept Slope -0.67 (0.02) 0.07 (0.03) LPM Logistic b. What is the predicted probability implied by the linear probability model for x=20 and x= 35? Note: Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places. Report the probability between 0 and 1 (not in %).

A random Variable X, from an unknown experiment produces the following Probability Mass Function Table: x 2 4 6 8 10 P(A) 1/4 a 1.8b 1:8 Given that the mean or the expected value of x is 6, E(x) = 6. Compute the coefficient of variation of the random variable x, CV(x)