The following attached questions are related to the topic Distribution of Random Variable.

I need the clarity in steps as i am getting the wrong answer while solving. So the exercise questions are attached below.

1. A shipment of 7 television sets contains 2 defectives. A hotel makes a random purchase of 3 of the sets. If X is the number of defective sets purchased by the hotel, find the mean of X. 2. The probability distribution of the discrete random variable X is f(x) = for x = 0, 1, 2, 3.10. Let X be a random variable with the following probability distribution: X -3 6 9 P(X = x) Find Max, where g(X) = (2X + 1)?5. Let X be a random variable with the following probability distribution: 0 2 3 P(X = x) Find the mean of X. 6. By investing in a particular stock, a person can make a profit in 1 year of $4000 with probability 0.4 or take a loss of $1000 with probability 0.7. What is this person's expected gain?20. The random variable X, representing the number of chocolate chips in a cookie, has the following probability distribution: 2 4 5 6 P(X = x) 0.01 0.25 0.4 0.3 0.04 Using Theorem 5.2, find the variance of X. 21. Referring to Exercise 9, find o for the function :(X) = 3X* + 4. 22. Find the standard deviation of the random variable ?(X) = (2X + 1) in Exercise 10.13. A continuous random variable X that can assume values between x = 2 and x = 5 has a density function given by f(x) = 2(1 + x)/27. (a) Find P(X