I need a answer and explanation about problem 7 and 8

4. Let X be the number of major storms in a particular state in a given year. The probability of having no major storms is 0.50, of one major storm is 0.30, of two major storms is 0.10, of three major storms is 0.08, and of four major storms is 0.02 (there have never been more than 4 major storms in this state in a given year). STA 103 Fall 2016 Homework 2 - Due Wednesday, October 12th 1. At a particular veterinarian school, 75% of all students are female. 60% of females play either computer games, console games, or both. 75% of males play either computer games, or console games, or both. Out of those who are female, 30% play computer games, and 10% play both console games and computer games. Out of those who are male, 20% play both computer games and console games, and 15% play console games only. (a) Write down the probability distribution of X in table form, and also check to make sure it is a valid probability distribution. (b) Find the expected number of major storms in a given year, and the standard deviation of the number of storms in a given year. (a) For women only, draw a representation of the sample space, and the numerical information you have. (b) Repeat part (a) for men. (c) Find the probability that there is at least 1 storm in a given year. (c) What is the probability that a female plays only console games? (d) If there was more than 1 storm, find the probability that there were 3 storms. (d) What is the probability that a male plays only computer games? 5. Let X be a continuous random variable defined on the interval [0, 4] with probability density function (e) What is the probability of picking a female, if they play both computer games and console games? p(x) = c(1 4x) (f) Is gender independent of playing computer games? Justify your answer. (a) Find the value of c such that p(x) is a valid probability density function. (b) Find the probability that X is greater than 3. 2. Suppose that start-up companies in the area of biotechnology have probability 0.20 of becoming profitable and that those in area of information technology have probability 0.15 of becoming profitable. Further assume that the start-up companies in biotechnology and information technology are independent. (c) If X is greater than 1, find the probability X is greater than 2. (d) What is the probability that X is less than some number a, assuming 0