A restaurant sells three sizes of shakes. The small, medium and large sizes each cost $ 2.00 $2.00dollar sign, 2, point, 00, $ 3.00 $3.00dollar sign, 3, point, 00, and $ 3.50 $3.50dollar sign, 3, point, 50 respectively. Let X XX represent the restaurant's income on a randomly selected shake purchase. Based on previous data, here's the probability distribution of X XX along with summary statistics: Small Medium Large X = income ($) X=income ($)X, equals, start text, i, n, c, o, m, e, space, left parenthesis, dollar sign, right parenthesis, end text 2.00 2.002, point, 00 3.00 3.003, point, 00 3.50 3.503, point, 50 P ( X ) P(X)P, left parenthesis, X, right parenthesis 0.28 0.280, point, 28 0.40 0.400, point, 40 0.32 0.320, point, 32 Mean: μ X = $ 2.88 μ X =$2.88mu, start subscript, X, end subscript, equals, dollar sign, 2, point, 88 Standard deviation: σ X ≈ $ 0.59 σ X ≈$0.59sigma, start subscript, X, end subscript, approximately equals, dollar sign, 0, point, 59 During the last hour of business, the restaurant offers a special that gives customers $ 1 $1dollar sign, 1 off any size shake. Assume that the special doesn't change the probability that corresponds to each size. Let Y YY represent their income on a randomly selected shake purchase with this special pricing. What are the mean and standard deviation of Y YY?