1. A bad marksman takes 12 shots at a target with probability of hitting the target with each shot of 0.2, independent of other shots. Z is the random variable representing the number of hits. a. Calculate and plot the PMF of Z. b. Calculate and plot CDF of Z. (You may desire to manually adjust the plot for our convention) c. What is the probability that 3 < z < 6 shots were hits? d. Find E[Z] and Var[Z] e. If the marksman were to get $x for each shot on target. How much should the marksman expect to get, in order to break even on the $50 entry fee?
![1. A bad marksman takes 12 shots at a target with probability of hitting the target with each shot of 0.2, independent of other shots. Z is the random variable representing the number of hits. a. Calculate and plot the PMF of Z. b. Calculate and plot CDF of Z. (You may desire to manually adjust the plot for our convention) c. What is the probability that 3 < z < 6 shots were hits? d. Find E[Z] and Var[Z] e. If the marksman were to get $x for each shot on target. How much should the marksman expect to get, in order to break even on the entry fee?](https://i0.wp.com/electricalstudent.com/wp-content/uploads/2022/05/1q-8.png?w=1170&ssl=1 "1. A bad marksman takes 12 shots at a target with probability of hitting the target with each shot of 0.2, independent of other shots. Z is the random variable representing the number of hits. a. Calculate and plot the PMF of Z. b. Calculate and plot CDF of Z. (You may desire to manually adjust the plot for our convention) c. What is the probability that 3 < z < 6 shots were hits? d. Find E[Z] and Var[Z] e. If the marksman were to get $x for each shot on target. How much should the marksman expect to get, in order to break even on the entry fee?")
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