refer to the attachments below

A coin is tossed twice. Let Z denote the number of heads on the first toss and W the total number of heads on the 2 tosses. Suppose the coin is unbalanced and a head has a 46% chance of occurring. Complete parts (a) through (d). (a) Find the joint probability distribution of W and Z. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals. Do not round.) O A W f(w,z) 0 2 Z N O B. f ( w , Z) 0 2 Z (b) Find the marginal distribution of W. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals. Do not round.) O A. W g(w) O B. g(w) (c) Find the marginal distribution of Z. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals. Do not round.) O A. Z 0 h(z O B. Z h(z (d) Find the probability that at least 1 head occurs. The probability that at least 1 head occurs is. (Type an integer or a decimal. Do not round.)The probability distribution of the discrete random variable X is given below. (x)= (3)(3) x = 0, 1, 2, 3. Find the mean of X. The mean of X is. (Type an integer or decimal rounded to three decimal places as needed.)If a dealer's profit, in units of $1000, on a new automobile can be looked upon as a random variable X having the density function below, find the average profit per automobile. 2 f ( x ) = 85 (11 -x), 0 0, 0 . elsewhere 9X The expected value of g(X) = e 10 is]. (Simplify your answer.)The random variable X, representing the number of errors per 100 lines of software code, has the following probability distribution. 2 3 5 6 (x ) 0.01 0.04 0.4 0.3 0.25 Use the following theorem to determine the variance of the random variable X. The variance of a random variable X is 62 = E (X2) - 12 The variance is . (Round to two decimal places as needed.)