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# A certain disease has an infection rate 1/5 in a rural area of 40 people. A sample of size 10 is taken at random without replacement. Let X be the...

A certain disease has an infection rate 1/5 in a rural area of 40 people. A sample of size 10 is taken at random without replacement. Let X be the number of infected people in the sample. (1) What is the distribution of X? Give the name of the distribution and values of the parameters; (2) List all the possible values of X;(3) Find the probability that exactly 2 individuals in the sample are infected by the disease;(4) Compute the mean and variance 2 of X using the formulas for this distribution;(5) Give a brief explanation of the formula for .