provide me complete solution of all parts please step by step all parts thanks

Q6 (11 points) Q6. (11pts) (Apply R to this question. Your solution should include R code and R output. R markdown should be used to present your solution) 1(3) For a rv X, its possible values are integers: 1, 2, 3, 4, 5. The distribution is p(1) = 0.1, p(2) = 0.1, p(3) = 0.3, p(4) = 0.3, P(5) = 0.2. Calculate the expected value and variance of X. 2(8). A phone-in health number receives, on the average, 8 calls per hour asking for health information. Let X be the Poisson random variable for the number of calls for any randomly selected one hour period. (a).(4) For the given Poisson distribution, simulate a random sample with sample size n = 1000, plot the histogram (relative frequency) for your random sample and add the true pmif plot to the same histogram plot. (b).(2) Compute the probability that in one hour there are exactly 3 calls. (c).(2) Compute the probability that in one hour there are 4 or more calls, + Drag and drop an image or PDF file or click to browse... Time left